If (x-1)2 = 400, which of the following could be the value of x-5?
Solution
Correct Answer: Option C
here, (x - 1)2 = 400
√(x - 1)^2 = √400
This gives us: |x – 1| = 20 Because there is an expression inside the absolute value sign, we must consider that the entire expression, and not just the variable, can be either positive or negative. We’ll need to solve the equation twice.
Solve for x-1 as positive:
|x – 1| = 20
x – 1 = 20
x = 21
Solve for x-1 as negative: |x – 1| = 20 or,-(x – 1) = 20 or,-x + 1 = 20 or,-x =19 or,x = -19 Thus, x – 5 can equal either 21 – 5 = 16 or -19 – 5 = -24.
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