Question

If x + y + z = 5, x² + y² + z² = 21 and y² = zx, then the value of y is:
1.  1/5
2. 2/5
3. 1/2
4. 1/4

Answer 1

Correct Answer - Option 2 : 2/5

Given:

x + y + z = 5

x² + y² + z² = 21

y² = zx

Formula used:

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

Calculations:

(x + y + z)² = 5²

⇒ x2 + y2 + z2 + 2(xy + yz + xz) = 25

⇒ 21 + 2(xy + yz + xz) = 25

⇒ 2(xy + yz + xz) = 25 - 21

⇒ xy + yz + xz = 4/2

⇒ xy + yz + xz = 2

⇒ xy + yz+ y² = 2

⇒ y(x + y + z) = 2

⇒ y(5) = 2

⇒ y = 2/5

∴ The required value of y = 2/5