Question

Mr. Smith's class took a short one question quiz. Dwight's calculation is shown below.
x^2=10
x= square root of 10
When the class switched papers to peer grade, Jonathan noticed that he had a different answer compared to Dwight.

Part A: Revise Dwight's calculation.

Part B: Explain why Dwight's original calculation was incorrect.

Could someone perhaps help me step by step to solve this problem? I'm completely lost.

Answer 1

correct steps:
x^2 = 10
± x = √10
x = ± √10

Answer 2

could you please explain that to me?

Answer 3

By the definition of the √ operator, we get the positive square root of the number
so when we have an equation such as x^2 = 4
there are two answers +2 or -1, BUT the negative answer comes from √(x^2) not from √4


this is best illustrated using an example such as
x^2 < 25, we intuitively know that correct answer is the set of all numbers between -5 and 5
that is, -5 < x < +5

The common error to solve this is this:
x^2 < 25
x < ± 5
which means x < -5 and x < +5, which would include such number as -10
but -10 is NOT a solution to the given inequality

the correct method is to use the ± with the x^2,
x^2 < 25
±x < 5
which means x < 5 and -x < 5
giving us : x < 5 and x > -5 or the correct solution of -5 < x < 5