What is sqrt(4x-3)= 2+sqrt(2x-5)?

2 Answers
Corvette G. ยท Stefan V.
Jul 11, 2018

x={3,7}

Explanation:

Given:

sqrt(4x-3)=2+sqrt(2x-5)

Square both sides:

sqrt(4x-3)^2=(2+sqrt(2x-5))^2

ACTUALLY square them:

4x-3=4+4sqrt(2x-5)+2x-5

Group like terms:

2x-2=4sqrt(2x-5)

Square both sides AGAIN:

4x^2-8x+4=16(2x-5)

Multiply:

4x^2-8x+4=32x-80

Group like terms:

4x^2-40x+84=0

Factor out 4:

4(x^2-10x+21)=0

Then

4(x^2 - 3x - 7x + 21) = 0

4[x(x-3)-7(x-3)] = 0

So

4(x-3)(x-7) = 0

Cem Sentin
Jul 11, 2018

x_1=3 and x_2=7

Explanation:

sqrt(4x-3)=2+sqrt(2x-5)

sqrt(4x-3)-sqrt(2x-5)=2

(sqrt(4x-3)-sqrt(2x-5))^2=2^2

4x-3+2x-5-2sqrt(8x^2-26x+15)=4

6x-12=2sqrt(8x^2-26x+15)

3x-6=sqrt(8x^2-26x+15)

(3x-6)^2=8x^2-26x+15

9x^2-36x+36=8x^2-26x+15

x^2-10x+21=0

(x-3)*(x-7)=0

Hence x_1=3 and x_2=7

Related questions
See all questions in Radical Equations
Impact of this question
6414 views around the world
You can reuse this answer
Creative Commons License