Question

Consider the equation StartRoot x plus 8 EndRoot equals 7 minus StartRoot x minus 6 EndRoot . Squaring the left side and simplifying results in​ _______. Squaring the right side and simplifying results in​ _______.

Answer 1

When we square the left side, we get x² + 16x + 64. When we square the right side, we get 49 - 14sqrt(x - 6) + (x - 6).

Step-by-step explanation:

When we square the left side of the equation, we use the property that the square root of a number squared is equal to the number itself.

So, squaring the left side, we get x + 8 squared, which simplifies to (x + 8)(x + 8) = x² + 16x + 64.

When we square the right side of the equation, we also use the property that the square root of a number squared is equal to the number itself.

So, squaring the right side, we get 7 - sqrt(x - 6) squared, which simplifies to (7 - sqrt(x - 6))(7 - sqrt(x - 6)) = 49 - 14sqrt(x - 6) + (x - 6).