Question

Find the non-extraneous solutions of the square root of the quantity x plus 9 minus 5 equals quantity x plus 4

Answer 1

I"m guessing you mean

`√(x+9) -5=x+4`
add 5 to both sides

`√(x+9)=x+9`
square both sides
x+9=x²+18x+81
minus x+9 both sides
0=x²+17x+72
factor
what 2 numbres multiply to get 72 and add to get 17?
8 and 9
0=(x+8)(x+9)
set to zer

0=x+8
x=-8

x+9=0
x=-9

test each


`√(-8+9) -5=-8+4`

`√(1) -5=-4`
1-5=-4
-4=-4
true


`√(-9+9) -5=-9+4`

`√(0) -5=-5`
-5=-5
true


the solutions are x=-9 and -8

Answer 2

x=8 and x=9

Explanation:

The given equation is:

`√(x+9)-5=x+4`

On solving this equation, we get

⇒
`√(x+9)=x+9`

Squaring on both sides, we get

⇒
`x+9=x^2+81+18x`

⇒
`x^2+18x-x-9+81=0`

⇒
`x^2+17x+72=0`

⇒
`x^2+8x+9x+72=0`

⇒
`(x+8)(x+9)=0`

Thus, the solution of the above equations are x= 8 and x=9.