How do you solve 4x^2 - 4x + 1 > 4 ?
First, consider solving the quadratic equation:
The first step is to collect all the terms together, leaving '=0' on the right hand side:
Solving by factorisation:
But we wish to solve the inequality:
Now consider a sketch of the graph y = 4x2 - 4x - 3 (right).
The graph (a 'U'-shaped parabola) shows that the function is greater than zero
to the left of the root at -0.5 and
to the right of the root at 1.5
So the solution to the equation x2 - 4x + 1 > 4 is:
x < -0.5 or x > 1.5