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

The answer to sqrt(x^2-1)=x-sqrt(x-1) is x= 5/4

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sqrt(x^2-1)=x-sqrt(x-1)

Solution

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

Solution

x = \frac{5}{4}

Decimal

x = 1.25

Solution steps

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

Square both sides:

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

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

Subtract

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

from both sides

x^{2} - 1 - (x^{2} - 2 x - 1 x + x - 1) = x^{2} - 2 x - 1 x + x - 1 - (x^{2} - 2 x - 1 x + x - 1)

Simplify

2 x - 1 x - x = 0

Factor

2 x - 1 x - x : x (2 x - 1 - 1)

x (2 x - 1 - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 2 x - 1 - 1 = 0

Solve

2 x - 1 - 1 = 0 : x = \frac{5}{4}

x = 0, x = \frac{5}{4}

Verify Solutions:

x = 0

False

, x = \frac{5}{4}

True

The solution is

x = \frac{5}{4}

Graph

Popular Examples

6-\sqrt[3]{x-5}=1

6 - 3 x - 5 = 1

x=1+sqrt(x^2+9)

x = 1 + x^{2} + 9

3x^{2/3}-20x^{1/3}-7=0

3 x^{\frac{2}{3}} - 20 x^{\frac{1}{3}} - 7 = 0

3sqrt(x-8)=19

3 x - 8 = 19

sqrt(30-x)+10=x

30 - x + 10 = x

Frequently Asked Questions (FAQ)

What is the answer to sqrt(x^2-1)=x-sqrt(x-1) ?
The answer to sqrt(x^2-1)=x-sqrt(x-1) is x= 5/4
Solve for x: sqrt(x^2-1)=x-sqrt(x-1)
The solution is x= 5/4

sqrt(x^2-1)=x-sqrt(x-1)

Solution

Solution

Graph

Popular Examples

Frequently Asked Questions (FAQ)

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

Solve for x: sqrt(x^2-1)=x-sqrt(x-1)