Question

Which equation results from taking the square root of both sides of (x – 9)2 = 81? x – 9 = ±9 x + 9 = ±9 x + 3 = ±9 x – 3 = ±9

Answer 1

Hello :
(x-9)² = 81

(x-9)² - 9² = (x-9-9)(x-9+9) =0
x-9-9=0 or x-9+9 =0
x-9 = 9 or x-9 =-9
coclusion :  x – 9 = ±9

Answer 2

Answer:- x-9=±9

Explanation:-

Given:-

$(x-9)^2=81\\\Rightarrow(x-9)^2-81=0\\\Rightarrow(x-9)^2-9^2=0\\\Rightarrow[(x-9)+9][(x-9)-9]=0.............by\ identity\ a^2-b^2=(a+b)(a-b)$

$\Rightarrow[(x-9)+9]=0\ or\ [(x-9)-9]=0\\\Rightarrow(x-9)=-9\ or\ (x-9)=9$

⇒x-9=±9

Thus on taking square root ob both sides of $(x-9)^2=81$, we get

$\sqrt{(x-9)^2}= \sqrt{81}$

$\\\Rightarrow(x-9)=\sqrt{9^2}$

⇒x-9=±9