Question

If x +y+z =5 ,xy + yz +zx = 5 then find x² +y² +z²​

Answer 1

Answer:

${x}^{2} + {y}^{2} + z {}^{2} = (x + y + z)^2 - 2(xy + yz + zx)$

$=5^2 -2 \times 5$

$=25-10$

$= 15$

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given -

• x + y + z = 5
• xy + yz + zx = 5

To Find -

• x² + y² + z²

Now,

→ x + y + z = 5

squaring both sides :-

→ (x + y + z)² = (5)²

→ x² + y² z² + 2(xy + yz + zx) = 25

→ x² + y² + z² = 25 - 2(5)

→ x² + y² + z² = 25 - 10

→ x² + y² + z² = 15

Hence,

The value of x² + y² + z² is 15.

Verification :-

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

→ (5)² = 15 + 2(5)

→ 25 = 25

LHS = RHS

Hence,

Verified...

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