Question

if X + Y + Z is equal to 8 and xy + Y Z plus ZX equal to 20 find value of x squared plus y squared + Z Square

Answer 1

Hi ,

x + y + z = 8-----( 1 )

xy + yz + zx = 20

Multiply each term with 2 , we get

2xy + 2yz + 2zx = 40 ---( 2 )

We know the algebraic identity ,

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

8² = x² + y² + z² + 40 [ from ( 1 ) & ( 2 )]

64 - 40 = x² + y² + z²

Therefore,

x² + y² + z² = 24

I hope this helps you.

:)