Question

Which statement describes if there is an extraneous solution to the equation √x-3 = x-5? A. there are no solutions to the equation, B. the extraneous solution is x = 7, C. the valid solutions are x = 7 and x = 4, or D. the extraneous solution is x = 4

Answer 1

x=4

Explanation:

did this on iready hope it helps

Answer 2

Remember that an extraneous solution of an equation, is the solution that emerges from solving the equation but is not a valid solution.

Lets solve our equation to find out what is the extraneous solution:

`√(x-3) =x-5`

`(√(x-3))^2 =(x-5)^2`

`x-3=x^2-10x+25`

`x^2-11x+28=0`

`(x-4)(x-7)=0`

`x-4=0` and
`x-7=0`

`x=4` and
`x=7`

So, the solutions of our equation are
`x=4` and
`x=7`. Lets replace each solution in our original equation to check if they are valid solutions:
- For
`x=7`

`√(x-3) =x-5`

`√(7-3) =7-5`

`√(4) =2`

`2=2`
We can conclude that 7 is a valid solution of the equation.

- For
`x=4`

`√(x-3) =x-5`

`√(4-3) =4-5`

`√(1) =1`

`1 \\eq 1`
We can conclude that 4 is not a valid solution of the equation; therefore, 4 is a extraneous solution.

We can conclude that the correct answer is: D. the extraneous solution is x = 4