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SSC CHSL 2023 PYQ — Question 70

SSC CHSL - 04 Aug 2023 - Shift 1 • Quantitative Aptitude • Q70

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Simplify the expression: (u−v)3+(v−w)3+(w−u)3(u2−v2)+(v2−w2)+(w2−u2)3\frac{(u-v)^3+(v-w)^3+(w-u)^3}{(u^2-v^2)+(v^2-w^2)+(w^2-u^2)^3}

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Correct answer: A

Explanation

The correct answer is Option 1 i.e 1(u+v)(v+w)(w+u)\frac{1}{(u+v)(v+w)(w+u)}.

we know that,

⇒ a2 - b2 = (a + b)(a - b)

⇒ a3 + b3 + c3 = 3abc if a + b + c = 0

⇒ (u−v)3+(v−w)3+(w−u)3(u2−v2)+(v2−w2)+(w2−u2)3\frac{(u-v)^3+(v-w)^3+(w-u)^3}{(u^2-v^2)+(v^2-w^2)+(w^2-u^2)^3}

⇒ (u - v) + (v - w) + (w - u) = 0

⇒ 3(u−v)+(v−w)+(w−u)3(u2−v2)+(v2−w2)+(w2−u2)\frac{3(u-v)+(v-w)+(w-u)}{3(u^2-v^2)+(v^2-w^2)+(w^2-u^2)}

⇒ (u−v)+(v−w)+(w−u)(u−v)(u+v)+(v−w)(v+w)+(w−u)(w+u)\frac{(u-v)+(v-w)+(w-u)}{(u-v)(u + v)+(v-w)(v + w)+(w-u)(w+u)}

⇒ 1(u+v)(v+w)(w+u)1\over{(u+v)(v+w)(w+u)}