2011-11-30, 04:11 AM
For the first one:
Divide both sides by 6
2 = sqrt(2x-1) - sqrt(x-4)
subtract sqrt(2x-1) from both sides
2 - sqrt(2x-1) = - sqrt(x-4)
change the signs to make it easier
sqrt(2x-1) - 2 = sqrt(x-4)
square both sides
2x - 1 - 4sqrt(2x-1) + 4 = x - 4
rearrange
2x+7-x = 4sqrt(2x-1)
square again
x^2 + 14x + 49 = 32x - 16
rearrange
x^2 - 18x + 65 = 0
quadratic formula GO
x = 5, 13 and the sum is 18
Divide both sides by 6
2 = sqrt(2x-1) - sqrt(x-4)
subtract sqrt(2x-1) from both sides
2 - sqrt(2x-1) = - sqrt(x-4)
change the signs to make it easier
sqrt(2x-1) - 2 = sqrt(x-4)
square both sides
2x - 1 - 4sqrt(2x-1) + 4 = x - 4
rearrange
2x+7-x = 4sqrt(2x-1)
square again
x^2 + 14x + 49 = 32x - 16
rearrange
x^2 - 18x + 65 = 0
quadratic formula GO
x = 5, 13 and the sum is 18