How do you solve $sqrt(x+2)-7=sqrt(x+9$ ?

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Answer 1 · 2017-04-23T11:47:27

No solutions exist.

$sqrt(x+2) - 7 = sqrt (x+9)$ . Squaring both sides , we get

$(cancelx+2) - 2*7*sqrt(x+2) +49 = (cancelx+9)$ or

$2-14 sqrt(x+2)+49 =9 or 14 sqrt(x+2)=42 or sqrt(x+2) =3$

Squaring both sides , we get $x+2 =9 or x=7$ [Ans]

Check:

$sqrt(7+2) - 7 = sqrt (7+9)$

$sqrt(9) - 7 = sqrt (16)$

$3 - 7 = 4$

$-4 = 4$

No solutions exist.

I entered the equation into a computation engine named, WolframAlpha ; it returned that no solutions exist.

How do you solve sqrt(x+2)-7=sqrt(x+9sqrt(x+2)-7=sqrt(x+9?