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

2 Answers

Answer:

#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#

Jul 11, 2018

Answer:

#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#