Michael J. answered • 10/27/15
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When solve equations that have radicals on both sides of equations, the goal is to eliminate all the radicals, so that the equation becomes easier to solve.
1)
Note that the left side of equation has everything under the radical. So we can square both sides of equation to undo the radical on that side.
2x + 5 = (2√(2x) + 1)(2√(2x) + 1)
2x + 5 = 4(2x) + 4√(2x) + 1
2x + 5 = 8x + 4√(2x) + 1
Next, is to isolate the radical term. Move all the non-radical terms to the left side of equation.
-6x + 4 = 4√(2x)
Now, we square both sides of equation. This will undo the last radical.
(-6x + 4)(-6x + 4) = 16 * 2x
36x2 - 48x + 16 = 32x
Subtract 32x on both sides of equation to get a quadratic equation.
36x2 - 80x + 16 = 0
Factor out a 4.
4(9x2 - 20x + 4) = 0
Set the term in parenthesis equal to zero.
9x2 - 20x + 4 = 0
Factor using FOIL, if possible.
(9x - 2)(x - 2) = 0
x = 2/9 and x = 2
We have two solutions. As a last step, you will need to plug in these x values into original equation to see if which one satisfies the equation.
Do the same for the second problem.
Michael J.
After you plug in x=2 into the original function, you evaluate both sides of equation to see if the left and right sides equal to each other. If you discover that the left side and right side of equation are not equal, then x=2 does not work, and we accept the other value.
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10/28/15
Bianca J.
Okay thanks! Now for #2, i tried doing it the same as you did, however im not sure how to square them
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10/28/15
Michael J.
The left side only has a radical term. So we can just square both sides of equation to undo the radical on that side.
y - 3 = (1 - √(2y - 4))(1 - √(2y - 4))
On the right side of equation, use FOIL to simplify.
y - 3 = 1 - 2√(2y - 4) + (2y - 4)
y - 3 = 2y - 3 - 2√(2y - 1)
From here, isolate the remaining radical term by moving all the non-radical terms to the left side of equation. Once you've done that, square both sides of equation to undo that last radical.
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10/28/15
Bianca J.
10/28/15