Solve : $x^{4} - 6 x^{2} + 4$

Open in App

Solution

$x^{4} - 6 x^{2} = 4$
Let $x^{2} = a$
$\Rightarrow a^{2} - 6 a + 4$
$\Rightarrow a = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
$\Rightarrow a = \frac{6 \pm \sqrt{36 - 4 (4)}}{2}$
$\Rightarrow a = \frac{6 \pm \sqrt{20}}{2} = \frac{6 \pm 2 \sqrt{5}}{2}$
$\Rightarrow a = 3 \pm \sqrt{5}$
So $x^{2} = 3 \pm \sqrt{5}$
$\Rightarrow x = \pm \sqrt{3 \pm \sqrt{5}}$ .

Suggest Corrections

Similar questions

x^{4} - 6 x^{2} - 16 = 0

x \frac{d y}{d x} = 2 y + x^{4} + 6 x^{2}

x \neq 0

x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 5 = 0

\sqrt{- 1}

Solve the equation $x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 5 = 0$ , given one root is $\sqrt{(- 1)}$ . Find the value of other three roots.

\frac{6 x^{2} - 5 x - 3}{x^{2} - 2 x + 6} \leq 4

Join BYJU'S Learning Program