Question

solve the quadratic equation
$3 x {}^{4} - 13x {}^{2} + 10 = 0$
​

Answer 1

Answer:

If you observe carefully it is

$3 {( {x}^{2} )}^{2} - 13 {x}^{2} + 10 = 0 \\ let \: \: {x}^{2} = y \\also \: \: note \: \: that \: \: \: y \geqslant 0 \\ 3 {y}^{2} - 13y + 10 = 0 \\ 3 {y}^{2} - 10y - 3y + 10 = 0 \\ (y - 1)(3y - 10) = 0 \\ \\ y = {x}^{2} = 1 \: \: \: \: and \: \: \: \: \frac{10}{3} \\ \\ \implies {x}^{} = \: \: \pm1 \: \: \: \: and \: \: \: \: \pm \sqrt{ \frac{10}{3} }$