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

The answer to sqrt(x+2\sqrt{x-1)}=2x-1 is x=1,x= 5/4

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

x + 2 x - 1 = 2 x - 1

x = 1, x = \frac{5}{4}

Decimal

x = 1, x = 1.25

Solution steps

x + 2 x - 1 = 2 x - 1

Remove square roots

4 x - 4 = 16 x^{4} - 40 x^{3} + 33 x^{2} - 10 x + 1

Solve

4 x - 4 = 16 x^{4} - 40 x^{3} + 33 x^{2} - 10 x + 1 : x = 1, x = \frac{5}{4}

x = 1, x = \frac{5}{4}

Verify Solutions:

x = 1

True

, x = \frac{5}{4}

True

The solutions are

x = 1, x = \frac{5}{4}

- x - 2 = x + 2

10 x - 6 = x + 1

9 x + 73 = x + 7

x + 1 = 8 - 4 x

4 x + 9 - 2 x + 1 = 2

What is the answer to sqrt(x+2\sqrt{x-1)}=2x-1 ?
The answer to sqrt(x+2\sqrt{x-1)}=2x-1 is x=1,x= 5/4
Solve for x: sqrt(x+2\sqrt{x-1)}=2x-1
The solution is x=1,x= 5/4