Question

What are the solutions of the equation 9x4 – 2x2 – 7 = 0? Use u substitution to solve.

Answer 1

C. x = ±i√7/9 and x = ±1

Explanation:

The correct answer to your question is C.

Answer 2

x = -1 or x = 1

Explanation:

`9x^4-2x^2-7=0\\\\9x^(2\cdot2)-2x^2-7=0\qquad\text{use}\ (a^n)^m=a^(n\cdot m)\\\\9(x^2)^2-2x^2-7=0\\\\\text{Substitute}:\ x^2=t\geq0\\\\9t^2-2t-7=0\\\\9t^2+7t-9t-7=0\\\\t(9t+7)-1(9t+7)=0\\\\(9t+7)(t-1)+0\iff 9t+7=0\ \vee\ t-1=0\\\\9t+7=0\qquad\text{subtract 7 from both sides}\\9t=-7\qquad\text{divide both sides by 9}\\t=-(7)/(9)<0\\\\t-1=0\qquad\text{add 1 to both sides}\\t=1`

`\text{Come back to the substitution}:\\\\t=1\to x^2=1\to x=\pm\sqrt1\\\\x=-1\ \vee\ x=1`