Question

If x + y + z = 9 and x² + y² + z² = 27 and (x + y + z)³ = 729. Find the value of (xy + yx + zx)/(x + y + z)
1. -9
2. 3
3. 6
4. -4

Answer 1

Correct Answer - Option 2 : 3

Given

x + y + z = 9

x2 + y2 + z2 = 27

(x + y + z)3 = 729

Formula used

(x + y + z)³ = (x + y + z){x² + y² + z² + 2xy + 2yz + 2zx}

Calculation

This is formula (x + y + z)3 = (x + y + z){x2 + y2 + z2 + 2xy + 2yz + 2zx}

⇒ 729 = 9({27 + 2(xy + yz + zx)}

⇒ 81 = 27 + 2(xy + yz + zx)

⇒ 54 = 2(xy + yz + zx)

⇒ (xy + yz + zx) = 27

(xy + yz + zx)/(x + y + z) = 27/9 = 3

∴ The required value of (xy + yx + zx)/(x + y + z) is 3.