SOLUTION: Hello. I am having problems with some problems. I was able to locate some on your site but am having trouble with a few others. Here is one: {{{ sqrt(2x-13)+sqrt(3x+4)=sqrt(5x+1)

Algebra ->  Radicals -> SOLUTION: Hello. I am having problems with some problems. I was able to locate some on your site but am having trouble with a few others. Here is one: {{{ sqrt(2x-13)+sqrt(3x+4)=sqrt(5x+1)       Log On


   

Question 32208: Hello. I am having problems with some problems. I was able to locate some on your site but am having trouble with a few others. Here is one:
+sqrt%282x-13%29%2Bsqrt%283x%2B4%29=sqrt%285x%2B1%29+. Any help that you can offer would be greatly appreciated.
Thank you,
Chris
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
+sqrt%282x-13%29%2Bsqrt%283x%2B4%29=sqrt%285x%2B1%29+...SQUARING BOTH SIDES
2X-13+3X+4+2* sqrt(2x-13)*sqrt(3x+4)=(5x+1)
2* sqrt(2x-13)*sqrt(3x+4)=5X+1-2X-3X+13-4=10
sqrt(2x-13)*sqrt(3x+4)=5..............SQUARING AGAIN....
(2x-13)*(3x+4)=25
6X^2+8X-39X-52=25
6X^2-31X-77=0
6X^2-42X+11X-77=0
6X(X-7)+11(X-7)=0
(X-7)(6X+11)=0
X-7=0...OR...X=7 .................6X+11=0...OR.....X=-11/6.........
SINCE WE SQUARED THE GIVEN EQN.TWICE ,IT IS NECESSARY TO CHECK WHETHER WE GOT THE CORRECT ANSWERS OR EXTRANEOUS SOLUTIONS.
PUT X=7...WE GET
+sqrt%282x-13%29%2Bsqrt%283x%2B4%29=sqrt%285x%2B1%29+
+sqrt%282%2A7-13%29%2Bsqrt%283%2A7%2B4%29=sqrt%285%2A7%2B1%29+.
1+5=6...OK.....
PUT X=-11/6...........THIS GIVES IMAGINARY NUMBERS..SO THIS IS NOT A SOLUTION.
HENCE X=7 IS THE ONLY ANSWER.