Question

Given (x – 1)2 = 50, select the values of x.

x=-49
x=51
x=1+5sqrt{2}
x=1-5sqrt{2}

Answer 1

C and D.

Explanation:

We want to solve the equation:

`(x-1)^2 = 50`

We can take the square root of both sides. Since we are taking an even root, we need plus/minus:

`\displaystyle (x-1) = \pm√(50)`

Note that:

`√(50) = √(2\cdot 5^2) = 5√(2)`

Hence:

`\displaystyle (x - 1) = \pm5√(2)`

And by adding one to both sides:

`\displaystyle x = 1 \pm 5√(2)`

In conclusion, our answers are both C and D.