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jmc

algebra intermediate

Problem

If

a

,

b

are nonzero real numbers such that

a^{2} + b^{2} = 8 ab

, find the value of

\frac{a + b}{a - b}

.

Solution

Note that

\frac{a + b}{a - b} = \frac{( a + b ) ^{2}}{( a - b ) ^{2}} = \frac{a ^{2} + b ^{2} + 2 ab}{a ^{2} + b ^{2} - 2 ab} = \frac{10 ab}{6 ab} = \frac{15}{3} .

Final answer

\frac{\sqrt{15}}{3}