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jmc

algebra intermediate

Problem

Compute

\frac{x ^{8} + 12 x ^{4} + 36}{x ^{4} + 6}

when

x = 5

.

Solution

Note that

(x^{4} + 6)^{2} = x^{8} + 12 x^{4} + 36

. So

\frac{x ^{8} + 12 x ^{4} + 36}{x ^{4} + 6} = \frac{( x ^{4} + 6 ) ^{2}}{x ^{4} + 6} = x^{4} + 6

. Our answer is therefore

5^{4} + 6 = 625 + 6 = 631

.

Final answer

631