Question

Determine the solution set of x^2-80=0.

Answer 1

x^2 - 80 = 0
x^2 = 80 ...take the square root of both sides, eliminating the ^2
x = (+-) sqrt 80
x = (+-) sqrt 16 * 5
x = (+-) 4 sqrt 5

so x = 4 sqrt 5 or x = -4 sqrt 5

Answer 2

Answer: The required solution set of the given equation is
`\{4\sqrt5,-4\sqrt5\}.`

Step-by-step explanation: We are given to determine the solution set of the following quadratic equation :

`x^2-80=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

Since the given equation does not contain the term involving x, so we will use the method of square root to solve the given equation.

The solution of equation (i) is as follows :

`x^2-80=0\\\\\Rightarrow x^2=80\\\\\Rightarrow x=\pm√(80)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow x=\pm√(16*5)\\\\\Rightarrow x=\pm4\sqrt5.`

Thus, the required solution set of the given equation is
`\{4\sqrt5,-4\sqrt5\}.`