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If x2 +y2 + z2 - 8x + 6y - 4z + 29 = 0, then find the value of z (x + y).
- A1
- B2
- C3
- D4
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CCommunity
x2 + y2 + z2 - 8x + 6y - 4z + 29 = 0
⇒ x2 - 8x + 16 + y2 + 6y + 9 + z2 - 4z + 4 = 0
⇒ (x - 4)2 + (y + 3)2 + (z - 2)2 = 0
So, putting the values of x = 4, y = -3 and z = 2 satisfies the above equation
∴ z(x + y) = 2 × (4 + (-3)) = 2
⇒ x2 - 8x + 16 + y2 + 6y + 9 + z2 - 4z + 4 = 0
⇒ (x - 4)2 + (y + 3)2 + (z - 2)2 = 0
So, putting the values of x = 4, y = -3 and z = 2 satisfies the above equation
∴ z(x + y) = 2 × (4 + (-3)) = 2