Question

Given that x + y = 5 and x² + y2 = 23. Find the value of x4 + y4.

Answer 1

Complete the pattern

20,12,4

Answer 2

Answer:

x⁴ + y⁴ = 527

Step-by-step explanation:

Given

x + y = 5

x² + y² = 23

To find

x⁴ + y⁴

Solution

(x + y)² = x² + y² + 2xy

(5)² = 23 + 2xy

25 = 23 + 2xy

2xy = 2

xy = 1

(x² + y²)² = x⁴ + y⁴ + 2x²y²

(23)² = x⁴ + y⁴ + 2xy(xy)

529 = x⁴ + y⁴ + 2

x⁴ + y⁴ = 527