Question Number 101436 by bobhans last updated on 02/Jul/20

Answered by bramlex last updated on 02/Jul/20

⇔ x^2 +30 + (√(x^2 +30)) = x^4 +x^2   set (√(x^2 +30)) = z  ⇔ z^2  + z = x^4  + x^2   (x^2 +z)(x^2 −z)+(x^2 −z) = 0  (x^2 −z)(x^2 +z+1)= 0  (1) x^2  = z = (√(x^2 +30))  x^4 −x^2 −30 = 0  (x^2 −6)(x^2 +5) = 0   x = ± (√6) ; x = ± i(√5) ⇐rejected  (2) x^2 +1 =−(√(x^2 +30)) ⇐ rejected  The Solution is x = ± (√6) ★