Question

Solve:

(x² – 3x)² – 16(x² – 3x) – 36 = 0

Answer 1

(x² – 3x)² – 16(x² – 3x) – 36 = 0

Let x² – 3x = y

Then y² – 16y – 36 = 0

`=>` y² – 18y + 2y – 36 = 0

`=>` y(y – 18) + 2(y – 18) = 0

`=>` (y – 18)(y + 2) = 0

If y – 18 = 0 or y + 2= 0

`=>` x² – 3x – 18 = 0 or x² – 3x + 2 = 0

`=>` x² – 6x + 3x – 18 = 0 or x² – 2x – x + 2 = 0

`=>` x(x – 6) + 3(x – 6) = 0 or x(x – 2) – 1(x – 2) = 0

`=>` (x – 6)(x + 3) = 0 or (x – 2)(x – 1) = 0

If x – 6 = 0 or x + 3 = 0 or x – 2 = 0 or x – 1 = 0

Then x = 6 or x = – 3 or x = 2 or x = 1