Question

x⁴+y⁴=8,x²+y²=4,then x+y=?​

Answer 1

solution

x+ y = 8

square on both side

(x+y)^2 = 8^2

x^2 + y^2 + 2 (xy) = 64

x^2 + y^2 + 2(12) = 64

x^2 + y^2 =64 - 24

x^2 + y^2 = 40

square again on both side

(x^2 + y^2)^2 = 40^2

x^4 + y^4 + 2( x^2 y^2) = 1600

x^4+y^4 + 2(12)^2 = 1600

x^4+y^4 + (2×144) = 1600

x^4+y^4 + 288 = 1600

x^4+y^4 = 1600 - 288

x^4+y^4 = 1312