What is the answer to sqrt(x^2-2x+1)-sqrt(x^2-4x+4)=x-3 ?

The answer to sqrt(x^2-2x+1)-sqrt(x^2-4x+4)=x-3 is x=4

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sqrt(x^2-2x+1)-sqrt(x^2-4x+4)=x-3

Solution

x^{2} - 2 x + 1 - x^{2} - 4 x + 4 = x - 3

Solution

x = 4

Solution steps

x^{2} - 2 x + 1 - x^{2} - 4 x + 4 = x - 3

Remove square roots

4 x^{4} - 40 x^{3} + 148 x^{2} - 240 x + 144 = x^{4} - 16 x^{3} + 88 x^{2} - 192 x + 144

Switch sides

2 x^{2} + 2 x^{2} - 4 x + 4 x - 10 x + 13 - 6 x^{2} - 4 x + 4 = x^{2} - 2 x + 1

Move

2 x^{2}

to the right side

2 x^{2} - 4 x + 4 x - 10 x + 13 - 6 x^{2} - 4 x + 4 = - x^{2} - 2 x + 1

Move

10 x

to the right side

2 x^{2} - 4 x + 4 x + 13 - 6 x^{2} - 4 x + 4 = - x^{2} + 8 x + 1

Move

13

to the right side

2 x^{2} - 4 x + 4 x - 6 x^{2} - 4 x + 4 = - x^{2} + 8 x - 12

Factor

2 x^{2} - 4 x + 4 x - 6 x^{2} - 4 x + 4 : 2 x^{2} - 4 x + 4 (x - 3)

2 x^{2} - 4 x + 4 (x - 3) = - x^{2} + 8 x - 12

Solve

4 x^{4} - 40 x^{3} + 148 x^{2} - 240 x + 144 = x^{4} - 16 x^{3} + 88 x^{2} - 192 x + 144 : x = 0, x = 2, x = 4

x = 0, x = 2, x = 4

Verify Solutions:

x = 0

False

, x = 2

False

, x = 4

True

The solution is

x = 4

Popular Examples

sqrt(x+7)-sqrt(3x-2)=1

x + 7 - 3 x - 2 = 1

x^{1/3}+2x^{2/3}-x=0

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

3sqrt(x-4)=12

3 x - 4 = 12

((2x+1))/((sqrt(4x^2-5)))=-1

\frac{( 2 x + 1 )}{( 4 x ^{2} - 5 )} = - 1

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

2 x - 1 = 3

Frequently Asked Questions (FAQ)

What is the answer to sqrt(x^2-2x+1)-sqrt(x^2-4x+4)=x-3 ?
The answer to sqrt(x^2-2x+1)-sqrt(x^2-4x+4)=x-3 is x=4
Solve for x: sqrt(x^2-2x+1)-sqrt(x^2-4x+4)=x-3
The solution is x=4

sqrt(x^2-2x+1)-sqrt(x^2-4x+4)=x-3

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to sqrt(x^2-2x+1)-sqrt(x^2-4x+4)=x-3 ?

Solve for x: sqrt(x^2-2x+1)-sqrt(x^2-4x+4)=x-3