Radicals are easy!

Algebra Level 4

Find the sum of roots of the following equation: x 2 − 12 x + x 2 − 12 x + 81 = 9 x^{2} - 12x + \sqrt{x^{2} - 12x +81}= 9 .


The answer is 12.

Shreya R by Shreya R , 21, India

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1 solution

Sai Ram
Aug 8, 2015

We denote that:

t = x 2 − 12 x + 81 → t 2 + t = 90 , t 2 + t − 90 = 0 t=\sqrt{x^{2}-12x+81} \rightarrow t^2+t=90, t^2+t-90=0

→ t = 9 , x 2 − 12 x = 0 → x = 0 , x = 12 \rightarrow t=9, x^{2}-12x=0 \rightarrow x=0, x=12

S u m = 12 Sum=\boxed{12}

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