To solve for x in the equation 3√(6x-1) - √(5x+1) = √3.6-1 - √3.5+1, we need to simplify and isolate x.
Starting with the left side of the equation:
3√(6x-1) - √(5x+1) = √3.6-1 - √3.5+1
We can simplify the square root terms on the right side:
3√(6x-1) - √(5x+1) = √(18-1) - √(15+1)
3√(6x-1) - √(5x+1) = √17 - √16
Now, we can square both sides of the equation to eliminate the square roots:
(3√(6x-1) - √(5x+1))^2 = (√17 - √16)^2
Expanding both sides:
(3√(6x-1))^2 - 2(3√(6x-1))√(5x+1) + (√(5x+1))^2 = (√17)^2 - 2√17√16 + (√16)^2
9(6x-1) - 2(3√(6x-1)√(5x+1)) + 5x+1 = 17 - 2√272 + 16
We can simplify the right side:
54x - 9 - 6√(6x-1)√(5x+1) + 5x + 1 = 17 - 2√272 + 16
Combining like terms:
59x - 8 - 6√(6x-1)√(5x+1) = 33 - 2√272
Now, we want to isolate the terms with square roots:
-6√(6x-1)√(5x+1) = -2√272
Dividing both sides by -2:
3√(6x-1)√(5x+1) = √272
Squaring both sides to eliminate square roots:
(3√(6x-1)√(5x+1))^2 = (√272)^2
9(6x-1)(5x+1) = 272
We can then expand and simplify:
270x^2 + 225x - 9 - 45 = 272
270x^2 + 225x - 54 = 272
Rearranging the equation:
270x^2 + 225x - 326 = 0
Now, we can solve this quadratic equation for x.