Question

(x+y+z)² + (x – y+z)^2+(x + y- z)^2​

Answer 1

Answer:

Given equations are x² + y² + z² = 525

xy + yz + zx = 50

Per algebraic identity.

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

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

= 525+2(50)

= 625

x+y+z = √625

= ±25

After squareroot will be cancelled , the number become ±25.

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

( ±25 )² = 525 + 2( 50 )

625 = 525 + 100

625 = 625

L.H.S = R.H.S.

So , the answer is ' ±25 '.