Question

If the value of sum of x and y is 7 and their product is 12, then find the value of x³ + y³.
1. 91
2. 81
3. 49
4. 93

Answer 1

Correct Answer - Option 1 : 91

Given:

x + y = 7

xy = 12

Formula Used:

a³ + b³ = (a + b) × (a² + b² - ab)

Calculations:

x + y = 7

Squaring both sides, we get

(x + y)² = 7²

⇒ x² + y² + 2xy = 49

⇒ x2 + y2 + 2 × 12 = 49      [xy = 12]

⇒ x2 + y2 = 25      ----(1)

a3 + b3 = (a + b) × (a2 + b2 - ab)

⇒ x³ + y³ = 7 × (25 - 12)

⇒ x3 + y3 = 91

∴ The value of (x3 + y3) is 91.