Question

If x + y + z = 22 and xy + yz + xz = 35, then what is the value of (x - y)² + (y - z)² + (z - x)² ?
1. 783
2. 671
3. 758
4. 772

Answer 1

Correct Answer - Option 3 : 758

Given:

x + y + z = 22

xy + yz + xz = 35

Formula used:

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

Calculation:

x + y + z = 22

xy + yz + xz = 35

According to the question,

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

⇒ (22)² = x2 + y2 + z2 + 2(35)

⇒ x2 + y2 + z² = 484 - 70

⇒ x2 + y2 + z2 = 414

Now,

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

⇒ 2(x2 + y2 + z2 - xy - yz - xz) = 2[x2 + y2 + z2 - (xy + yz + xz)] 

⇒ 2(414 - 35)

⇒ 2 × 379 = 758

∴ The value of (x - y)2 + (y - z)2 + (z - x)2 is 758.