If x + y + z = 0, then what will be the value of ((x²)/yz)+((y²)/zx)+((z²)/xy)?

If x + y + z = 0, then what will be the value of…

If x + y + z = 0, then what will be the value of $(\frac{x^2}{yz})+(\frac{y^2}{zx})+(\frac{z^2}{xy})?$

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 3

Calculations:

We know that, x + y + z = 0 and

x³ + y³ + z³ = 3xyz

⇒ $(\frac{x^2}{yz})+(\frac{y^2}{zx})+(\frac{z^2}{xy})$

⇒ $\frac{x^3 + y^3 + z^3}{xyz}$

⇒ $\frac{3xyz}{xyz}$

⇒ 3