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

Equations with a quadratic hidden inside them

Substitute complex terms with simpler variable (e.g., $u$)

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

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

Square roots must be positive

$x = pmsqrt{3}$

$x = 4$

No, square numbers cannot be negative

After substitution, $u$ values are negative (no real $x$)

Substitute back to find original variable

Substitute $u = x^2$ to get $u^2 - 5u + 6 = 0$