Answer to Question #123087 in Algebra for Hussain Ousman Darboe

Question

For what value of x; x^4+4x^2+x+8/x^2+4/x^4 is a complete square where x is not zero

Answer 1

x⁴+4x²+x+8/x²+4/x²=x⁴+4/x⁴+4-4+x+4x²+8/x²

as

x⁴+4/x⁴+4=(x²+2/x²)² : 4x²+8/x²=4(x²+2/x²)

we get

(x²+2/x²)²+4(x²+2/x²)-4+x

complete square

(x²+2/x²)²+4(x²+2/x²) +4

where from 4=-4+x

x=8