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SSC CGL 2021 PYQ — Question 63

SSC CGL - 18 Aug 2021 - Shift 2 • Quantitative Aptitude • Q63

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If a + b + c = 0, then what is the value of (b+c)2bc+(c+a)2ca+(a+b)2ab=?\frac{(b+c)^2}{bc}+\frac{(c+a)^2}{ca}+\frac{(a+b)^2}{ab}=?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 3

⇒ (b+c)2bc+(c+a)2ca+(a+b)2ab\frac{(b+c)^2}{bc}+\frac{(c+a)^2}{ca}+\frac{(a+b)^2}{ab}

 ⇒ a(b+c)2abc+b(c+a)2abc+c(a+b)2abc\frac{a(b+c)^2}{abc}+\frac{b(c+a)^2}{abc}+\frac{c(a+b)^2}{abc}

Let  b + c = -a , a + c = -b and a + b = -c.

⇒ a3+b3+c3abc\frac{a^3 + b^3 + c^3}{abc}= (a+b+c)(a2+b2+c2−ab−bc−ca)+3abcabc\frac{(a+b+c)(a^2+b^2+c^2-ab-bc-ca) + 3abc}{abc} 

Here a + b + c = 0

So, (a+b+c)(a2+b2+c2−ab−bc−ca)+3abcabc\frac{(a+b+c)(a^2+b^2+c^2-ab-bc-ca) + 3abc}{abc} = 0.