Description:
Simplification questions involve complicated equations with few variables.
Approach:
Solve these questions by changing the form of the equations given until
variables cancel out or a familiar outcome becomes apparent.
1) Square roots
If an equation has square roots, eliminate them by squaring both sides of
the equation
For example:
(4x - 4)1⁄2 = x
Squaring both sides of the equation yields
(4x - 4) = x2.
Moving terms to one side of the equation yields the quadratic equation
x2 - 4x + 4
which can be factored;
(x - 2)2 = 0
2) Squares
If an equation has squares, eliminate them by taking the square root of
both sides.
For example:
4x2
= 9y2
Taking the square root of both sides the equation yields
2x = 3y.
Now y
can be solved directly in terms of x;
y = 2⁄3 * x
Remember that when you you solve for a square there are usually two
solutions.
If y2 = 9
and you take the square root of
both sides the resulting equation is y = 3.
However, y can equal 3 or -3.
3) Practice:
-
What value of x
satisfies the equation
(2x - 1)2
= x4?
-
What value of x
satisfies the equation
(4x - 4)1⁄2
= x?
