Question

Which equation is equivalent to?

Answer 1

For this case we must find an equation equivalent to:

`\sqrt {x ^ 2 + 81} = x + 10`

We square both sides of the equation to eliminate the root:

`x ^ 2 + 81 = (x + 10) ^ 2`

We have by definition that:

`(a + b) ^ 2 = a ^ 2 + 2ab + b ^ 2`

So, rewriting the right side of the equation we have:

`x ^ 2 + 81 = x ^ 2 + 2 * 10 * x + 10 ^ 2\\x ^ 2 + 81 = x ^ 2 + 20x + 100`

ANswer:

Option D