What is the answer to sqrt(2x-5)-sqrt(x-3)=3 ?

The answer to sqrt(2x-5)-sqrt(x-3)=3 is x=29+6sqrt(17)

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sqrt(2x-5)-sqrt(x-3)=3

2 x - 5 - x - 3 = 3

x = 29 + 617

Decimal Notation

x = 53.73863 \dots

Solution steps

2 x - 5 - x - 3 = 3

Remove square roots

x^{2} - 22 x + 121 = 36 x - 108

Solve

x^{2} - 22 x + 121 = 36 x - 108 : x = 29 + 617, x = 29 - 617

x = 29 + 617, x = 29 - 617

Verify Solutions:

x = 29 + 617

True

, x = 29 - 617

False

The solution is

x = 29 + 617

x^{4} = (x + 7)^{2}

x^{2} = 1

4 x = 2 3 - x

3 - 2 x = 7

12 x^{4} - 96 x^{\frac{13}{4}} = 0

What is the answer to sqrt(2x-5)-sqrt(x-3)=3 ?
The answer to sqrt(2x-5)-sqrt(x-3)=3 is x=29+6sqrt(17)
Solve for x: sqrt(2x-5)-sqrt(x-3)=3
The solution is x=29+6sqrt(17)