SOLUTION: {{{ sqrt ( 2x-1 )+ sqrt ( 2-x ) =2

Algebra ->  Radicals -> SOLUTION: {{{ sqrt ( 2x-1 )+ sqrt ( 2-x ) =2      Log On


   

Question 955053: sqrt ( 2x-1 )+ sqrt ( 2-x ) =2
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282x-1%29%2B+sqrt%282-x%29=2
sqrt%282x-1%29=2-+sqrt%282-x%29
2x-1=4-4sqrt%282-x%29%2B%282-x%29
2x-1=6-x-4sqrt%282-x%29
3x-7=-4sqrt%282-x%29
9x%5E2-42x%2B49=16%282-x%29
9x%5E2-42x%2B49=32-16x
9x%5E2-26x%2B17=0
%28x-1%29%289x-17%29=0
Two solutions:
x-1=0
x=1
and
9x-17=0
9x=17
x=17%2F9
.
.
Checking,
sqrt%282%281%29-1%29%2Bsqrt%282-1%29=2
sqrt%282-1%29%2Bsqrt%281%29=2
1%2B1=2
2=2
True, good solution.
.
.
.
sqrt%282%2817%2F9%29-1%29%2Bsqrt%282-17%2F9%29=2
sqrt%2834%2F9-9%2F9%29%2Bsqrt%2818%2F9-17%2F9%29=2
sqrt%2825%2F9%29%2Bsqrt%281%2F9%29=2
5%2F3%2B1%2F3=2
6%2F3=2
2=2
True, good solution.