Question

If x2 + y2 + z2 + 6x - 4y + 16z + 29 = 0,then find the value of x + 2y - z.
1. 5
2. 11
3. 6
4. 7

Answer 1

Correct Answer - Option 1 : 5

Given:

x² + y² + z² + 6x - 4y + 16z + 29 = 0

Formula Used:

(x + y)² = x2 + y2 + 2xy

Calculations:

x2 + y2 + z2 ​+ 6x - 4y + 16z + 29 = 0

⇒ x² + 2 × 3x + 9 + y2 - 2 × 2y + 4 + z² + 2 × 4z + 16 = 0

⇒ (x + 3)² + (y - 2)² + (z + 4)² = 0

⇒ (x + 3)² = 0, (y - 2)² = 0, (z + 4)² = 0

⇒ x = -3, y = 2, z = -4

Now, x + 2y - z = -3 + 2 × 2 - (-4)

⇒ x + 2y - z = -3 + 4 + 4 

⇒ x + 2y - z = 5

∴ The value of x + 2y - z is 5.