If x + y + z = 0, then what is the value of \({{x^2} \over (yz)}\) + \({{y^2} \over (xz)}\) + \({{z^2} \over (xy)}\)?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 03 Dec 2022 Shift 4)

Answer 1

Given:

x + y + z = 0

Concept used:

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

If x + y + z = 0, then

x³ + y³ + z³ - 3xyz = 0

So, x3 + y3 + z3 = 3xyz

Calculation:

\({{x^2} \over (yz)}\) + \({{y^2} \over (xz)}\) + \({{z^2} \over (xy)}\)

⇒ \({{x^3 + y^3 + z^3} \over (xyz)}\)

⇒ \({{3xyz} \over xyz}\)

⇒ 3

∴ The required answer is 3.

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