Question

Which statement about square root x-5 - square root x = 5 is true?

a) x = –3 is a true solution.
b) x = –3 is an extraneous solution.
c) x = 9 is a true solution.
d) x = 9 is an extraneous solution.

Answer 1

Hello,

Answer D


`√(x-5) - √(x) =5`
==>
`(x-5) -2*√((x-5)x)+x =25`
==>
`2x-30=√(x(x-5))`
==>
`x-15=√(x(x-5))`
==>
`x^2-30x+225=x(x-5)`
==>
`225=-5x+30x`
==>
`25x=225`
==>
`x=9`
But:


`√(9-5) - √(9)=√(4) - √(9)=2-3=-1`≠5

Step-by-step explanation:


`\lim_(x \to \infty) √(x-5)- √(x)`


`= \lim_(x \to \infty) \frac{(√(x-5)- √(x))*(√(x-5)+ √(x))} {√(x-5)+ √(x)}`


`= \lim_(x \to \infty) ((-5))/(√(x-5)+ √(x))`


`= \lim_(x \to \infty) (-5)/(\infty)=0`