If x + y + z = 0, then what is the value of X² over (YZ)+Y² over (XZ)+Z² over (XY) ?

If x + y + z = 0, then what is the value of X² over…

If x + y + z = 0, then what is the value of ${{X^2} \over (YZ)}+{{Y^2} \over (XZ)}+{{Z^2} \over (XY)}$ ?

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 3.

Given:

x + y + z = 0

Concept Used:

If x + y + z = 0, then x³ + y³ + z³ = 3xyz ....(i)

Explanation:

According to the given question,

x²/(yz) + y²/(xz) + z²/(xy)

⇒ (x³ + y³ + z³)/xyz = 3xyz/xyz = 3 {Using equation (i)}

Hence the required value is 3.