Question

(x - 5) 2 = 81

Which of the following expressions represents the solutions to the given equation?


-5 ± √(81)

5 ± √(81)

-25 ± √(81)

Answer 1

Option 2nd is correct

`5 \pm √(81)`

Explanation:

Given the equation:

`(x-5)^2 = 81`

Taking square root both sides we have;

`√((x-5)^2)= \pm √(2)`

Using the exponent rule:

`\sqrt[n]{x^n}=x`

then;

`x-5 = \pm √(81)`

Add 5 to both sides we have;

`x-5+5= 5 \pm √(81)`

Simplify:

`x = 5 \pm √(81)`

Therefore, the following expressions represents the solutions to the given equation is,
`5 \pm √(81)`

Answer 2

`(x-5)^2=81\to x-5=\pm√(81)\ \ \ |+5\\\\x=5\pm√(81)`

Answer: 5 ± √(81)