Answer 1

(x² – x)² + 5(x² – x)+ 4=0

Let `x^2 - x = y`

Then `y^2 + 5y + 4 = 0`

`=> y^2 + 4y + y + 4 = 0`

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

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

if y + 4 = 0  or y + 1 = 0

`=> x^2 - x + 4 = 0 or x^2 - 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