Question

If x³ + y³ = 468 and x + y = 12, then the value of x⁴ + y⁴ will be:
1. 2036
2. 3025
3. 3620
4. 3026

Answer 1

Correct Answer - Option 4 : 3026

Given:

x³ + y³ = 468

x + y = 12

Calculations:

x⁴ + y⁴ = (x² + y²)² - 2x²y²    ......(1)

x³ + y³ = (x + y) (x² + y² - xy)

468/12 = (x² + y² - xy)   

39 = (x² + y² - xy)    ......(2)

(x+y)² = x² + y² + 2xy

144 = x² + y² + 2xy

x² + y² = 144 - 2xy    ......(3)

Putting x² + y² in equ.(2)

 39 = (144 - 2xy - xy)

We get xy = 35 & x² + y² = 74

Now,

x⁴ + y⁴ = (74)² - 2(35)²

⇒ 5476 - 2450

⇒ 3026

∴ The correct choice is option 4.