SOLUTION: sqrt(7x+1)-sqrt(5x+4)=1

Question 884241: sqrt(7x+1)-sqrt(5x+4)=1

Found 2 solutions by Fombitz, Theo:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

Two solutions:

and

Verifying the solutions:

False, not a real solution.

True.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your equation is:
sqrt(7x+1)-sqrt(5x+4)=1
add sqrt(5x+4) to both sides of the equation to get:
sqrt(7x+1) = 1+sqrt(5x+4)
square both sides of the equation to get:
7x+1 = 1 + 2*sqrt(5x+4) + 5x+4
combine like terms to get:
7x+1 = 2*sqrt(5x+4) + 5x + 5
subtract 5x and 5 from both sides of the equation to get:
2x-4 = 2*sqrt(5x+4)
divide both sides of the equation by 2 to get:
x-2 = sqrt(5x+4)
commute this equation to get:
sqrt(5x+4) = x-2
square both sides of this equation to get:
5x+4 = x^2 -4x + 4
subtract 5x and 4 from both sides of this equation to get:
0 = x^2 - 9x
commute this equation to get:
x^2 - 9x = 0
factor this equation to get:
x * (x-9) = 0
solve for x to get:
x = 0 or x = 9
substitute these answers in the original equation to confirm whether the solutions are good or not.

substituting 0 gets:
sqrt(1) - sqrt(4) = 1 which becomes:
1 - 2 = 1 which becomes:
1 = 3 which is not true, therefore x = 0 is not a solution.

substituting 9 gets:
sqrt(64) - sqrt(49) = 1 which becomes:
8 - 7 = 1 which becomes:
1 = 1 which is true, therefore x = 9 is a solution.

the solution is x = 9.

RELATED QUESTIONS
how do you solve the following: {{{sqrt(x+4)}}} + {{{sqrt(2x-1)}}} = {{{sqrt(7x+1)}}} (answered by tracyc0912,Edwin McCravy)
SQRT(7x+25) = x + 1 (answered by tommyt3rd,stanbon)
Sqrt(5x+1)=Sqrt(x-2)... (answered by jim_thompson5910)
1. sqrt (45x-90) + sqrt (5x-10)= (answered by reviewermath)
Sqrt(5x+1)-sqrt(x)=5 (answered by jim_thompson5910)
please!!!!!!!! {{{(1/(sqrt(1) + sqrt(2)))+(1/(sqrt(2) + sqrt(3)))+(1/(sqrt(3) +... (answered by psbhowmick)
Please find the solution of: {{{ sqrt(5x+1) + sqrt(3x+4) = sqrt(16x+9)... (answered by Edwin McCravy)
{{{sqrt(4x+1)-sqrt(2x+4)=1}}} (answered by Theo)
sqrt (x-1)= 4 sqrt... (answered by fractalier)