Question

if x+y+z=8,xy+yz+zx=20, find x²+y²+z²​

Answer 1

-32 is the correct answer!

property used ==>

(x+y+z)² = x²+y²+z²+2(xy+yz+zx)

hope it helps you friend!

Answer 2

Answer:

Hence, the value of x^2 + y^2 + z^2 is 24.

Step-by-step explanation:

Given:-

x + y + z = 8

and

xy + yz + zx = 20

To find out:-

Value of x^2 + y^2 + z^2

Solution:-

We have,

x + y + z = 8

Squaring on both sides, we get

→ (x + y + z)^2 = (8)^2

→ x^2 + y^2 + z^2 + 2xy + 2yz + 2zx = 64

→ x^2 + y^2 + z^2 + 2(xy + yz + zx) = 64

→ x^2 + y^2 + z^2 + 2(20) = 64

[ ∵ xy + yz + zx = 20]

→ x^2 + y^2 + z^2 + 40 = 64

→ x^2 + y^2 + z^2 = 64 - 40

→ x^2 + y^2 + z^2 = 24

Answer:-

Hence, the value of x^2 + y^2 + z^2 is 24.

:)