x + y + z = 0 అయితే, \({{x^2} \over (yz)}\)+\({{y^2} \over (xz)}\)+\({{z^2} \over (xy)}\) విలువ ఎంత?

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

Option 4 : 3
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Detailed Solution

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ఇవ్వబడింది:​

x + y + z = 0

ఉపయోగించిన భావన:​

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

x + y + z = 0 అయితే, అప్పుడు

x3 + y3 + z3 - 3xyz = 0

కాబట్టి, x3 + y3 + z3 = 3xyz

లెక్కింపు:​

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

⇒ \({{x^3 + y^3 + z^3} \over (xyz)}\)

⇒ \({{3xyz} \over xyz}\)

⇒ 3

∴ అవసరమైన సమాధానం 3.

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