यदि x + y + z = 0 है, तो \({{x^2} \over (yz)}\) + \({{y^2} \over (xz)}\) + \({{z^2} \over (xy)}\) का मान क्या है?

Question

Question

This question was previously asked in

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

Answer 1

दिया गया है:

x + y + z = 0

प्रयुक्त अवधारणा:

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

यदि x + y + z = 0, तो

x3 + y3 + z3 - 3xyz = 0

So, x3 + y3 + z3 = 3xyz

गणना:

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

⇒ \({{x^3 + y^3 + z^3} \over (xyz)}\)

⇒ \({{3xyz} \over xyz}\)

⇒ 3

∴ अभीष्ट उत्तर 3 है।