How many solutions are there to the equation x^2 = 1? Explain how you know.

Question

asked Sep 21, 2020 90.5k views

1 Answer

Duhanebel · Answer 1 · 2020-09-26T13:27:40+0000

Answer:

Two solutions

Explanation:

Let's clear the variable x.

Since x is squared we apply square root to clear

$x^2=1\\√(x^2)= 1$

We have the following term
√(x^2)

This term corresponds to the formula of a absolute value of a number.

The absolute value of a number is its distance from zero on a number line

$x^2=1\\√(x^2)= 1\\\|x\|=1$

$x=1\\x=-1$

the absolute value of x is equal to 1 this means that x takes all the values that are at a distance of one unit from zero on the real line

The numbers that have a distance of 1 unit from zero would be 1 and also -1 (as it is a distance the module is always positive)