Question

If $4x^4-20x^2+9=0$ ,then x = _____

• A. $\pm \frac{1}{\sqrt{2}},\pm \frac{\sqrt{3}}{2}$
• B. $\pm \frac{1}{\sqrt{2}},\sqrt{\frac{3}{2}}$
• C. $\pm \frac{1}{\sqrt{2}},\pm \frac{3}{2}$
• D. $\pm \frac{1}{\sqrt{2}},\pm \frac{3}{\sqrt{2}}$

Answer 1

The correct option is D $\pm \frac{1}{\sqrt{2}},\pm \frac{3}{\sqrt{2}}$

Let $x^2=a$

So, the given eqn becomes $4a^2-20a+9=0$

$=>4a^2-2a-18a+9=0$

$=>2a(2a-1)-9(2a-1)=0$

$=>(2a-1)(2a-9)=0$

$=>a=\frac{1}{2};\frac{9}{2}$

So, $x^2=\frac{1}{2};\frac{9}{2}$

$=>x=\pm \frac{1}{\sqrt{2}};\pm \frac{3}{\sqrt{2}}$