SarkariPYQ

SSC CHSL 2023 PYQ — Question 72

SSC CHSL - 07 Aug 2023 - Shift 4 • Quantitative Aptitude • Q72

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Simplify the given expression: x3+y3+z3−3xyz(x−y)2+(y−z)2+(z−x)2x^3+y^3+z^3-3xyz\over(x-y)^2+(y-z)^2+(z-x)^2

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 12(x+y+z)\frac{1}{2}(x+y+z).Figure for the explanation of question 72

x3+y3+z3−3xyz(x−y)2+(y−z)2+(z−x)2x^3+y^3+z^3-3xyz\over(x-y)^2+(y-z)^2+(z-x)^2

We know that,

x3 + y3 + z3 - 3xyz = (x + y + z)(x2 + y2 + z2 - xy - yz - zx)

So,

⇒ Figure for the explanation of question 72(x+y+z)(x2+y2+z2−xy−yz−zx)(x2+y2−2xy)+(y2+z2−2yz)+(z2+x2−2zx)(x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)\over(x^2+y^2-2xy)+(y^2+z^2-2yz)+(z^2+x^2-2zx)

⇒ (x+y+z)(x2+y2+z2−xy−yz−zx)2(x2+y2+z2−xy−yz−zx)(x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)\over2(x^2+y^2+z^2 -xy-yz-zx)

⇒ (x+y+z)2(x + y + z)\over2