Square both sides to get:
2x+4 = 6x+1 - 2√(6x+1) + 1
transpose terms without the square-root radical to the left, and everything else to the right and divide both sides by the common factor 2:
2√(6x+1) = 6x+1 -(2x+4) + 1
√(6x+1) = 2x - 1
Square again:
6x+1 = 4x² - 4x + 1
4x² -10x=0
x(x-5)=0
Solve for x to get x=0 or x=5
Since we squared two times, it is possible that we have introduced solutions which are not acceptable. To eliminate the invalid solutions, substitute each value into the original equation and check if the solution works.
x=0 gives √(4)=√(1)-1
which clearly does not work, so it is rejected.
x=5/2 gives √(5+4)=√(15+1)-1
which is valid.
So x=5/2.
Solve the following equation
1) root(2x+4)= root(6x+1) -1
1 answer
2 answers