Question

For the following equation, determine the values of the missing entries. Reduce all fractions to lowest terms.x = y²Note: Each column in the table represents an ordered pair. If multiple solutions exist, you only need to identify one.

Answer 1

Given the equation:

`x=y^2`

Solving for y:

`y=√(x)`

If we are given the values of y, we use the first equation, otherwise, we use the second equation.

We are required to find the values of y for x ={0, 16, 100} and the values of x for:

`y={}\lbrace√(5),-2√(2)\rbrace`

Calculate the values of y:

x = 0

`y=√(0)=0`

x = 16

`y=√(16)=4`

x = 100

`y=√(100)=10`

Now calculate the values of x.

`x=(√(5))^2=5`

Finally:

`\begin{gathered} x=(-2√(2))^2 \\ \\ x=(-2)^2(√(2))^2 \\ \\ x=4\cdot2=8 \end{gathered}`

The table with the completed values is shown below: