Question

plz answer with explanation

Answer 1

x + y = 8
square both side

(x+y)² = (8)²

x² + y² + 2xy = 64

x² + y² + 2(12) = 64

x² + y² + 24 = 64

x² + y² = 64-24

x² + y² = 40

then ,

x⁴ + y⁴

= (x²)² + (y²)²

= (x²+y²)² - 2x²y²

[cause a²+b² = (a+b)² - 2ab]

= (40)² - 2(XY)²

= 1600 - 2(12)²

= 1600 -2(144)

= 1600 - 288

= 1312

so , x⁴ + y⁴ = 1312