Video: Solving Cubic Equations and Linear Equations Involving Roots

If (𝑥³, 𝑦 − 4) = (−8, √4), find the values of 𝑥 and 𝑦.

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Video Transcript

If the ordered pair or coordinate 𝑥 cubed, 𝑦 minus four is equal to negative eight, root four, find the values of 𝑥 and 𝑦.

For the ordered pairs or coordinates to be equal, they must be written in the same order. Therefore, 𝑥 cubed is equal to negative eight. And 𝑦 minus four is equal to the square root of four. The inverse of cubing is cube rooting. Therefore, in the first equation, we need to cube-root both sides.

The cube root of 𝑥 cubed is equal to 𝑥. On the right-hand side, we have the cube root of negative eight. The cube root of any negative number is always negative. In this case, the cube root of negative eight is equal to negative two. This is because negative two cubed or negative two multiplied by negative two multiplied by negative two is equal to negative eight. We therefore have a value for 𝑥 equal to negative two.

In the second equation, the positive square root of four is equal to two as two multiplied by two equals four. Our final step here is to add four to both sides of the equation. Two plus four is equal to six. Therefore, our value for 𝑦 is equal to six.

If the ordered pair 𝑥 cubed, 𝑦 minus four is equal to negative eight, root four, then 𝑥 is equal to negative two and 𝑦 is equal to six.

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