Question

help

Answer 1

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

Answer 2

\[\sqrt{x + 9 } - 5 = x +4\]
looks like this ^

Answer 3

ok! now please note that yor radicand has to be positive or equals to zero:
namely\[x+9\ge 0\]
or:
\[x \ge -9\]
so our non-extraneous solutions are those which are Greaterthan or equal to -9

Answer 4

this is incase you want to see the multiple choice along with the question

Answer 5

now squaring both sides of your equation, I got:
\[x+9=(x+9)^{2}\]
so:
\[(x+9)^{2}-(x+9)=0\]
then:
\[(x+9)[x+9-1]=0\]
finally:
\[(x+9)(x+8)=0\]
Now if I apply the canceling law of product, I will get:
x=-9, and x=-8
since both solutions check the inequality \[x \ge-9\]
we can say that aour non-extraneous solutions are:
x=-9,
x=-8

Answer 6

so D. namely the fourth option

Answer 7

Thank you so much and i wasn't sure about this because i'm not good in the square roots but i really appreciate your help

Answer 8

if there is something not clear, tell me, please!

Answer 9

I will because your good at explaining so thank you

Answer 10

thank you!

Answer 11

np :) okay i'm going to try to finish my homework and ill let you know if i need anything

Answer 12

ok!