Question

If X + y + z= 15 and x square + y square + z square = 75, find xy + yz + zx

Answer 1

Question:-

If x + y + z = 15 and x² + y² + z² = 75 , find xy + yz + zx

Solution:-

By using this identity.

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

Now,

x + y + z = 15

x² + y² + z² = 75

xy + yz + zx = ?

Put the value of formula

( 15 )² = 75 + 2 ( xy + yz + xz )

225 = 75 + 2 ( xy + yz + xz )

225 - 75 = 2 ( xy + yz + xz )

150 = 2 ( xy + yz + xz )

( xy + yz + xz ) = 150/2

( xy + yz + xz ) = 75

Answer:-

value of ( xy + yz + xz ) is 75