Question

Please help!

Solve the equation.
√3x-5-3√x = 0
x = -
[?

Answer 1

x = 7

x = 2

√ 3x − 5 = x − 3

or

3x − 5 = ( x − 3 ) 2

or

3x − 5 = x 2 − 6x + 9

or

x 2 − 9x + 14 = 0

or

x 2 − 7x − 2x + 14 = 0

or

x(x − 7) − 2(x − 7) = 0

or

(x − 7) ( x − 2) = 0

or

x − 7 = 0

or

x = 7

Ans

1

or

x − 2 = 0

or

x = 2

Ans

2

Answer 2

The solution to the equation √3x - 5 - 3√x = 0 is x = 5/6. After checking, this value satisfies the original equation.

To solve the equation with the square root terms, √3x - 5 - 3√x = 0, the first step is to isolate one of the radical terms. By adding 3√x to both sides, we get √(3x - 5) = 3√(x).

Next, squaring both sides eliminates the square root, resulting in (√(3x - 5))^2 = (3√(x))^2. Simplifying gives 3x - 5 = 9x.

Rearranging the equation, we have 5 = 6x. Solving for x yields x = 5/6. However, it's crucial to verify this solution by substituting it back into the original equation.

Upon checking, when x = 5/6, both sides of the equation are indeed equal, confirming that x = 5/6 is the solution.