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

The answer to sqrt(x-\sqrt{2x+3)}=1 is x=2+sqrt(6)

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sqrt(x-\sqrt{2x+3)}=1

x - 2 x + 3 = 1

x = 2 + 6

Decimal Notation

x = 4.44948 \dots

Solution steps

x - 2 x + 3 = 1

Remove square roots

2 x + 3 = 1 - 2 x + x^{2}

Solve

2 x + 3 = 1 - 2 x + x^{2} : x = 2 + 6, x = 2 - 6

x = 2 + 6, x = 2 - 6

Verify Solutions:

x = 2 + 6

True

, x = 2 - 6

False

The solution is

x = 2 + 6

2 t + 5 = - 5

x + 2 = 3 x - 5 - 1

x - x + 1 = 0

5 x - 6 - 16 = 0

What is the answer to sqrt(x-\sqrt{2x+3)}=1 ?
The answer to sqrt(x-\sqrt{2x+3)}=1 is x=2+sqrt(6)
Solve for x: sqrt(x-\sqrt{2x+3)}=1
The solution is x=2+sqrt(6)