Question
Download Solution PDFIf x + y + z = 0, then what is the value of \({{x^2} \over (yz)}\) + \({{y^2} \over (xz)}\) + \({{z^2} \over (xy)}\)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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.
Last updated on Jul 10, 2025
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