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jmc

algebra intermediate

Problem

If

m + \frac{1}{m} = 8

, then what is the value of

m^{2} + \frac{1}{m ^{2}} + 4

?

Solution

Squaring the equation provided, we get

m^{2} + 2 (m) (\frac{1}{m}) + \frac{1}{m ^{2}} = 64,

so

m^{2} + \frac{1}{m ^{2}} + 4 = 66

.

Final answer

66