Please solve and show your work.  Solve (x-4)^2 = 3.

Expert Answers

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You may use the alternate method such that:

` (x-4)^2 = 3 =>  (x-4)^2 - 3 = 0 =>  (x-4)^2 - (sqrt3)^2 = 0`

You need to convert the difference of squares into a product using the following formula such that:

`a^2 - b^2 = (a - b)(a + b)`

Reasoning by analogy yields:

`(x-4)^2 - (sqrt3)^2 = (x - 4 - sqrt3)(x - 4 + sqrt3)`

Since `(x-4)^2 - (sqrt3)^2 = 0` , then `(x - 4 - sqrt3)(x - 4 + sqrt3) ` `= 0` , hence, you need to solve the following equations such that:

`{(x - 4 - sqrt3 = 0),(x - 4+ sqrt3 = 0):}=> {(x= 4+ sqrt3),(x= 4- sqrt3):}`

Hence, evaluating the solutions to the given equation yields `x = 4 +sqrt3`  and `x = 4 - sqrt3.`

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