Question

if x+y=8 ,xy=12 then x^4+y^4= ? please

Answer 1

x+y =8

Square on both sides,

(x+y)² =8²

x² +y² +2(xy) =64

x² +y² +2(12) =64

x²+y² = 64-24

x²+y² = 40

Square again on both sides,

(x²+y²)² =(40)²

x⁴+y⁴+2(x²y²) =1600

x⁴+y⁴ +2(xy)² =1600

x⁴+y⁴ +2(12)² =1600

x⁴+y⁴+{2×144} =1600

x⁴+y⁴ +288 =1600

x⁴+y⁴ =1600-288

x⁴+y⁴ = 1312