Question

what is the value of the given expression​

Answer 1

Question :-

If x + y + z = 9 and xy + yz + zx then find the value of (x² + y² + z²).

Answer :-

Value of x² + y² + z² is 35.

Explanation :-

We know that

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

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

Here

• x + y + z = 9

• xy + yz + zx = 23

By substituting the given values in the above equation

⇒ (9)² = x² + y² + z² + 2(23)

⇒ 81 = x² + y² + z² + 46

⇒ 81 - 46 = x² + y² + z²

⇒ 35 = x² + y² + z²

⇒ x² + y² + z² = 35

∴ the value of x² + y² + z² is 35.

Answer 2

Answer:

35

Explanation:

1) ( x + y + z )²

= x² + y² + 2² + 2xy + y² + zx

2) ( x + y + z )²

= x² + y² + Z² + 2 ( xy + yz + zx )

Then:

→ x + y + z

→xy + yz + zx = 23

Adding values to equation:

→ ( 9 )² = x² + y² + z² + 2 ( 23 )

→ 81 = x² + y² + 2² + 46

→ 81 - 46 = x² + y² + z²

→ 35 = x² + y² + z²

→ x² + y² + z² = 35

Therefore, 35 is the answer.