Solve √x+20+ √x+4=4√x-1
Answers
Step-by-step explanation:
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How do you solve
√
x
+
4
−
√
x
−
4
=
2
?
Algebra Radical Equations
1 Answer
George C.
Mar 15, 2018
x
=
5
Explanation:
Given:
√
x
+
4
−
√
x
−
4
=
2
Squaring both sides, we get:
(
x
+
4
)
−
2
√
x
+
4
√
x
−
4
+
(
x
−
4
)
=
4
That is:
2
x
−
2
√
x
2
−
16
=
4
Divide both sides by
2
to get:
x
−
√
x
2
−
16
=
2
Add
√
x
2
−
16
−
2
to both sides to get:
x
−
2
=
√
x
2
−
16
Square both sides to get:
x
2
−
4
x
+
4
=
x
2
−
16
Add
−
x
2
+
4
x
+
16
to both sides to get:
20
=
4
x
Transpose and divide both sides by
4
to get:
x
=
5
Since we have squared both sides of the equation - which not a reversible operation - we need to check that this solution we have reached is a solution of the original equation.
We find:
√
(
5
)
+
4
−
√
(
5
)
−
4
=
√
9
−
√
1
=
3
−
1
=
2
So
x
=
5
is a valid solution.
Answer link
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