What is the solution set to the equation: x-3=(5x-1)^1/2

Question

A) {10}

B) {1, 10}

Answer 1

x - 3 = √(5x - 1)

 

(x - 3)² = 5x - 1

 

x²- 6x + 9 = 5x - 1

 

x² - 11x + 10 = 0

 

(x - 10)(x - 1) = 0

 

x = 10 or x = 1

 

Checking in the original equation, we see that 1 doesn't work and 10 does work.  The only solution is {10}.  

Answer 2

The fractional exponent 1/2 indicates a square-root.

 

x - 3 = √(5x - 1)

 

 

Square both sides of the equation to undo the square-root symbol.

 

(x - 3)² = 5x - 1

 

 

Expand the left side.

 

x² - 6x + 9 = 5x - 1

 

 

Subtract 5x and add 1 on both sides of equation.

 

x² - 11x + 10 = 0

 

 

Factor using FOIL.

 

(x - 10)(x - 1) = 0

 

 

Set the factors equal to zero.

 

x - 10 = 0              and               x - 1 = 0

 

x = 10                   and                x = 1

 

 

Pick the answer choice that matches this solution.