Question

If x + y +z = 0, then show that x^2 + y^2 + z^2 = -2 (xy + yz + xz)?

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

We are aware of the identity that

$(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca$

CALCULATION

Using the above mentioned Identity we get

$(x + y + z)² = x² + y² + z² + 2xy + 2yz+ 2zx$

Now x + y + z = 0 gives

$(0)² = x² + y² + z² + 2xy + 2yz+ 2zx$

$\therefore \: x² + y² + z² = - ( 2xy + 2yz+ 2zx)$

$\therefore \: x² + y² + z² = - 2( xy + yz+ zx)$