What is the answer to sqrt(2x+3)-2sqrt(x-2)=1 ?

The answer to sqrt(2x+3)-2sqrt(x-2)=1 is x=3

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sqrt(2x+3)-2sqrt(x-2)=1

2 x + 3 - 2 x - 2 = 1

x = 3

Solution steps

2 x + 3 - 2 x - 2 = 1

Remove square roots

4 x^{2} - 40 x + 100 = 16 x - 32

Solve

4 x^{2} - 40 x + 100 = 16 x - 32 : x = 11, x = 3

x = 11, x = 3

Verify Solutions:

x = 11

False

, x = 3

True

The solution is

x = 3

x^{2} + 6 x = 13 x^{2} + 6 x - 36

5 - 4 x - x = 0

\frac{2 x + 3}{x - 1} = x

2 x = 4

x + 1 = x + 13

What is the answer to sqrt(2x+3)-2sqrt(x-2)=1 ?
The answer to sqrt(2x+3)-2sqrt(x-2)=1 is x=3
Solve for x: sqrt(2x+3)-2sqrt(x-2)=1
The solution is x=3