Question

Solve:

(x² – x)² + 5(x² – x) + 4 = 0

Answer 1

(x² – x)² + 5(x² – x) + 4 = 0

Let x² – x = y

Then y² + 5y + 4 = 0

`=>` y² + 4y + y + 4 = 0

`=>` y(y + 4) + 1(y + 4) = 0

`=>` (y + 4)(y + 1) = 0

If y + 4 = 0 or y + 1 = 0

`=>` x² – x + 4 = 0 or x² – x + 1 = 0

`=> x = (-(-1)+-sqrt((-1)^2 - 4(1)(4)))/(2(1))` or `(-(-1) +- sqrt((-1)^2 - 4(1)(1)))/(2(1))`

`=> x = (1 +- sqrt(-15))/2 ("reject")` or `x = (1 +- sqrt(-3))/2 ("reject")`

∴ Given equation has no real solution