Question

$x {4} - 9x ^{2} - 10 = 0$

Answer 1

${\text{The, given equation is bi-quadratic equation, which can be solved using middle term splitting}}. \hfill \\ {x^4} - 9{x^2} - 10 = 0 \hfill \\ \Rightarrow {x^4} - 10{x^2} + {x^2} - 10 = 0 \hfill \\ \Rightarrow \left( {{x^2} + 1} \right)\left( {{x^2} - 10} \right) = 0 \hfill \\ \Rightarrow \left( {{x^2} + 1} \right) = 0{\text{ }} \Rightarrow x = \pm \sqrt { - 1} = \pm i \notin R \hfill \\ {\text{or }}\left( {{x^2} - 10} \right) = 0 \Rightarrow x = \pm \sqrt {10} \in R$

{\text{ is the required real solution}}{\text{.}}