Question

solve for x
${x}^{2} + {x}^{4 } = 90$

Answer 1

x^2 + x^4 = 90

=> x^4 + x^2 - 90 = 0

Let x^2 = a

=> a^2 + a - 90 = 0

=> a^2 + 10a - 9a - 90 = 0

=> a (a +10) - 9( a +10) = 0

=> (a+10)(a-9) = 0


a = - 10 and 9

Neglecting negative value,

a = 9

=> x^2 = 9

=> x = +3 and - 3

Answer 2

Given Equation is x^2 + x^4 = 90

x^2 + x^4 - 90 = 0

x^4 + x^2 - 90 = 0

x^4 - 9x^2 + 10x^2 - 90 = 0

x^2(x^2 - 9) + 10(x^2 - 9) = 0

(x^2 - 9)(x^2 + 10) = 0

$x = 3, -3 (or) \sqrt{10}i, - \sqrt{10} i$


Hope this helps!