for what value of m, x4+4x2+m+8/x2+4/x4 is a complete square where x is not equal to 0

Answer 1

x^4 + 4x^2 + m + 8/x^2 + 4/x^4

well, we will have

(x^2 + k + 2/x^2)^2

x^4 + kx^2 + 2 + + kx^2 + k^2 + 2k/x^2 + 2 + 2k/x^2 + 4/x^4

x^4 + 2kx^2 + 4 + k^2 + 4k/x^2 + 4/x^4

equate like powers of x to find that we must have k=2

so m = 4+k^2 = 8