Answer The Formula for x³ y³ z³ can be derived from the formula of x³ y³ z³ 3xyz x³ y³ z³ 3xyz = (x y z) (x² y² z² – xy – yz– zx) In order to find the formula of x³ y³ z³, we need to send 3xyz to the right side of equal signProve that the equation $x^3y^3z^33xyz=1$ defines a surface of revolution and find the analytical equation of its axis of revolution I think that I need to apply What must be subtracted from 4x^42x^36x^22x6 so that the result is exactly divisible by 2x^2x1?
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X^3+y^3+z^3-3xyz formula-There are two formula of it 1 x^3 y^3 z^3 3xyz = (xyz) (x^2y^2z^2xyyzzx) 2 x^3 y^3 z^3 3xyz = (1/2) (xyz) {xy)^2(yz)^2(zx)^2}Find the value of x3 y3 z3 3xyz if x y z 12 and x2y2z270 Hint Here, we have to find the value of the algebraic expression We will find the value of the sum of the product of the variables by substituting the given equation in the square of the sum of the three variables' identity
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Answer is (xy z)(x^2 y^2 xyz z^2) You can check by multiplying it out Notice that each term is a perfect cube x^3 y^3 = (xy)^3 So we have a sum of cubes, and the factoring formula is a^3 b^3 = (ab)(a^2abb^2) So we use a = xy and b = z to get x^3 y^3 z^3 = (xy)^3 z^3 = ((xy) z)((xy)^2(xy)zz^2) =(xy z)(x^2 y^2 xyz z^2) check by multiplying itThe algebraic identities for class 9 consist of identities of all the algebraic formulas and expressions You must have learned algebra formulas for class 9, which are mathematical rule expressed in symbols but the algebraic identities represent that the equation is true for all the values of the variables For example; $$\underbrace{x^3y^3}z^33xyz = \underbrace{(xy)^33xy(xy)}z^33xyz$$ $$=\underbrace{(xy)^3z^3}\underbrace{3xy(xy)3xyz} $$ $$=\underbrace{\{(xy)z\}}\{(xy)^2(xy)zz^2\}3xy\underbrace{\{(xy)z\}} \left(\text{ using } a^3b^3=(ab)(a^2abb^2)\text{ for the first two terms }\right) =(xyz)\{(xy)^2(xy)zz^2
Let us consider LHS of the equation LHS = x 3 y 3 z 3 – 3xyz LHS = 1 3 2 3 3 3 – 3(1 × 2 × 3) LHS = 1 8 27 – (3 ×6) LHS = 36 – 18In this question, we will partially differentiate u two times to find the value of k Complete stepbystep answer Now, we will use partial differentiation It is denoted by ∂ We are given u = log ( x 3 y 3 z 3 3xyz) So, partially differentiating u with respect to x, we get ∂ u ∂ x = 3 x 2 3yz ( x 3 y 3 z 3 3xyz)(x^3 y^3 z^3) = (x y z)^3 3{(x)(y)(xy) (y)(z)(yz) (z)(x)(zx)} 6(x)(y)(z) Substituting z for (xy) etc , respectively in the second parenthesis, the RHS reduces to 0 9(x)(y)(z) 6(x)(y)(z) = 3(x)(y)(z)
You can put this solution on YOUR website!Solution x = 2x, y = 2y and z = 4z If x y z = 0, then x 3 y 3 z 3 = 3xyz 8x 3 27y 3 64z 3 = 3 (2x) (2y) (4z) = 48xyz After having gone through the stuff given above, we hope that the students would have understood, "x cube plus y cube plus z cube minus 3xyz" Apart from the stuff given in this section, if you need any other Hint Use the expansion formula of $ {(x y)^3} $ Then replace $ y $ with $ y z $ to write it in three variables Then replace $ y $ with $ y z $ to write it in three variables Further expand it using the condition given in the question and simplify it in the terms of the required result
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Answer (1 of 7) First of all, we observe the following formula {{\left( a\,\,b \right)}^{\,3}}\,=\,{{a}^{\,3}}\,\,{{b}^{\,3}}\,\,3\,a\,b\,\left( a\,\,b \right $\begingroup$ By your factorization you could get $\frac{x^{3}y^{3}z^{3} 3xyz}{x y z} xy yz xz = x^{2} y^{2} z^{2}$ Then using a derivative test you can find the minimum $\endgroup$ –X^3y^3z^33xyz= (xyz) (x^2y^2z^2xyyzzx)/a^3b^3c^33abc= (abc) (a^2b^2c^2abbcca) Watch later Share Copy link Info Shopping Tap
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X 3 y 3 z 3 = { (x y z) × (x 2 y 2 z 2 xy yz zx)} 3xyzFormula of polynomials If the polynomial k 2 x 3 − kx 2 3kx k is exactly divisible by (x3) then the positive value of k is ____= 30y 2(x y3)9 (Note Chain rule again, and second term has no y) 3 If z = f(x,y) = xexy, then the partial derivatives are ∂z ∂x = exy xyexy (Note Product rule (and chain rule in the second term) ∂z ∂y = x2exy (Note No product rule, but we did need the chain rule) 4 If w = f(x,y,z) = y xyz, then the partial derivatives are
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When you are clear with the logic behind every formula, solving any kind of problem become easier If you are perfect with all the belowmentioned formulas in Maths for Class 9 that is listed chapterwise, nothing can stop you from scoring maximum marks in the final examination ( x^{3} y^{3} z^{3} – 3xyz = (x y z)(x^{2} y^{2(xyz) (x ^ 2 xy y ^ 2 xzyz z ^ 2) หลักฐาน โปรดทราบว่า x = y z เป็นคำตอบของ x ^ 3y ^ 3z ^ 33xyz = 0 เสียบ x = y z ในสมการข้างต้น (y z) ^ 3y ^ 3z ^ 33 (y z) yz = y ^ 3 3y ^ 2z 3yz ^ 2 z ^ 3 y ^ 3z ^ 33y ^ 2z3yz ^ 2 = 0 เราจึงสามารถหารThe formula of x 3 y 3 z 3 – 3xyz is written as \(x^{3} y^{3} z^{3} – 3xyz = (x y z) (x^{2} y^{2} z^{2} – xy – yz – zx)\) Let us prove the equation by putting the values of x = 1;
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Calculation ⇒ x 3 y 3 z 3 3xyz = 1/2 × (255 256 257) × (255 256) 2 (256 257) 2 (257 255) 2 Stay updated with the Quantitative Aptitude questions & answers with Testbook Know more about Algebra and ace the concept of Identities(x1) (x2) = x 2 3x 2We know that the formula, x3 y3 z3 −3xyz = (xyz)(x2 y2 z2 −xy−yz−xz) Put the all value in above formula, we get x3 y3 z3 −3xyz = 12×(70−37) = 12×33 =
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Now, From the second formula x 3 y 3 z 3 3xyz = (x y z)(x 2 y 2 z 2 xy yz zx) ⇒ 12 3xyz = 6(x 2 y 2 z 2 ) (xy yz zx) ⇒ 12 3xyz = 610 13(xyz)^3 (x y z)(x y z)(x y z) We multiply using the FOIL Method x * x = x^2 x * y = xy x * z = xz y * x = xy y * y = y^2Answer The formula of x 3 y 3 z 3 – 3xyz is written as x3y3 z3–3xyz = (xyz)(x2y2z2–xy–yz–zx) x 3 y 3 z 3 – 3 x y z = ( x y z) ( x 2 y 2 z 2 – x y – y z – z x) Let us prove the equation by putting the values of x = 1 y = 2 z = 3 Let us consider LHS of the equation LHS = x 3 y 3 z 3 – 3xyz
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If x y z = 0, show that x^3 y^3 z^3 = 3xyz (with Video) Ex 25, 13If x y z = 0, show that x3 y3 z3 = 3xyz We know that x3 y3 z3 3xyz = (x y z) (x2 y2 z2 xy yz zx) Putting x y z = 0,x3 y3 z3 3xyz = (0) (x2 y2 z2 xy yz zx)x3 y3 z3 3xyz = 0 x3 y3 z3 = 3xyz Hence pro First We take RHS & use the Formula ( ab)²= a²b²2ab & simplify it then RHS becomes equal to LHS RHS ⇒ 1/2×(x y z) (x² y²2xy y² z²2yzx²z²2xz) Given x y z = 3, x2 y2 z2 = 45 and x3 y3 z3 = 69 Formula used (x y z)2 = x2 y2 Win over the concepts of Algebra and get a step ahead with the preparations for Quantitative Aptitude with Testbook
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Factor x^3y^3 x3 − y3 x 3 y 3 Since both terms are perfect cubes, factor using the difference of cubes formula, a3 −b3 = (a−b)(a2 abb2) a 3 b 3 = ( a b) ( a 2 a b b 2) where a = x a = x and b = y b = y (x−y)(x2 xyy2) ( x y) ( x 2 x y y 2)Learn about Algebra Formula, Equations and List of Basic Algebraic Formulas & Expression in Math Algebra includes real numbers, complex numbers, matrices, vectors and many other topicsBy plugging it into WolframAlpha I've learned that it's $$(xy)(xz)(yz)(xyz)$$ My question is Stack Exchange Network Stack Exchange network consists of 178 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
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Factor x 3 y 3 z 3 − 3 x y z x^3 y^3 z^3 3xyz x 3 y 3 z 3 − 3 x y z The above polynomial is a symmetric polynomial because you can switch any two variables and still get the same polynomial যদি x = 1, y = 2 এবং z = 3 এর মান সন্ধান করে (i) `x^(3) y^(3) z^33xyz` (II) `3xy^(4) 15 x^(2) y 4z` Books Physics NCERT DC Pandey Sunil Batra HC Verma Pradeep Errorless Chemistry NCERT P Bahadur IITJEE Previous Areas of Parallelograms and Triangles Circles Coordinate Geometry Herons Explanation Calling f (x,y,z) = x3 y3 3xyz − 3 = 0 The gradient of f (x,y,z) at point x,y,z is a vector normal to the surface at this point The gradient is obtained as follows ∇f (x,y,z) = (f x,f y,f z) = 3(x2 yz,y2 xz,xy) at point (1,2, −1) has the value 3( −1,3,2) and the unit vector is { − 1,3,2} √1 32 22 = { −
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Given x = 7, y = 8, and z = 9 Formula used x3 y3 z3 3xyz = (1/2)(x y z)(x y)2 (y z)2 (z x)2 Cal If `xyz=0` show that `x^3y^3z^3=3x y z`Solution (By Examveda Team) Given, x y z = 0 Cubing both side, (x y z) 3 = 0 x 3 y 3 z 3 3xyz = 0 using formula x 3 y 3 z 3 = 3xyz
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x 3 y 3 z 3 3xyz = (xy) 3 3x 2 y 3xy 2 z 3 3xyz = (xy) 3 z 3 3xy (xyz) = (xyz) (xy) 2 z (xy) z 2 3xy (xyz) = (xyz) (x 2 2xyy 2 xzyzz 2 3xy) = (xyz) (x 2 y 2 z 2 xyyzzx) bởi Nguyễn Thanh Huyền Like (1) Báo cáo sai phạm Cách tích điểm HP If `xy=z` prove that `x^(3)y^(3)3xyz=z^(3)` CBSE Class 10 term 1 result 21 in January Know how to Calculate marks, result download process, result date, result time and other details hereThis one is a bit tricky, but anyways Let WLOG x ≤ y ≤ z and let y = a x, z = b x Now plug this into Now this is linear in x Hence we may take x = 0 to achieve the minimum of LHS This gives We take a = t b with t ≥ 1 Then C max = min t ≥ 1 t 3 1 t ( t − 1) Which I
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