Question

Which equation results from taking the square root of both sides (x-9)^2=81

Answer 1

`\bold{x-9=\pm 9}` is the equation that results.

Explanation:

Step 1:

`(x-9)^(2)`=81.

=>
`(x-9)^(2)` - 81 = 0

=>
`(x-9)^(2) -9^(2)`= 0

Step 2:

=> [( x - 9) + 9][( x-9)-9]=0 by the identity
`a^(2)-b^(2)`=(a + b) (a-b)

=> [( x - 9) + 9] = 0 or [( x - 9) - 9] = 0

=> ( x - 9) = - 9 or ( x - 9) = 9

=> x – 9 = ± 9

Step 3:

By taking square root on both side of
`(x-9)^(2)`= 81, we get

`\begin{array}{l}{\sqrt{(x-9)^(2)}=√(81)} \\ {=>(x-9)=\sqrt{9^(2)}} \\ {\Rightarrow x-9=\pm 9}\end{array}`

Answer 2

x - 9 = ±9

Explanation:

We have been given the following equation;

(x-9)^2=81

We are to determine the resulting equation after taking the square root of both sides.

The square root of the expression in the left hand side is;

((x-9)^2)^(1/2)

The square and square root are inverse functions and as such they simply cancel out yielding;

x-9

Now, the square root of 81 is simply ±9 since 9*9 = 81;

9^2 = 81

Thus the square root of 81 is ±9. The resulting equation is thus;

x - 9 = ±9

This can be simplified by adding 9 on both sides of the equation to yield;

x - 9 + 9 = 9 ± 9

x = 9 ± 9

x = 9 + 9 = 18 or x = 9 - 9 = 0

x = 18 or x = 0