Further Solving Quadratic Equations (Hidden Quadratics) (AQA A-Level Mathematics): Flashcards

Equations with a quadratic hidden inside them

Substitution with simpler variable like $u$

$u = x^2$, so $u^2 = x^4$

$u = \sqrt{x}$, so $u^2 = x$

Substitute, Solve for $u$, Substitute back

$x = \pm\sqrt{3}$

$x = 4$

Square roots must be non-negative ($\geq 0$)

No real roots

Square numbers cannot be negative