Which equation is equivalent to?
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For this case we must find an equation equivalent to:
[tex]\sqrt {x ^ 2 + 81} = x + 10[/tex]
We square both sides of the equation to eliminate the root:
[tex]x ^ 2 + 81 = (x + 10) ^ 2[/tex]
We have by definition that:
[tex](a + b) ^ 2 = a ^ 2 + 2ab + b ^ 2[/tex]
So, rewriting the right side of the equation we have:
[tex]x ^ 2 + 81 = x ^ 2 + 2 * 10 * x + 10 ^ 2\\x ^ 2 + 81 = x ^ 2 + 20x + 100[/tex]
ANswer:
Option D