Problem on Equation | AMC-10A, 2007 | Problem 20

Suppose that the number \(a\) satisfies the equation \(4 = a + a^{ – 1}\). What is the value of \(a^{4} + a^{ – 4}\)?

Given that \(4 = a + a^{ – 1}\). we have to find out the value \(a^{4} + a^{ – 4}\)

Squarring both sides of \(a^{4} + a^{ – 4}\) …then opbtain…

can you finish the problem……..

\((a + a^{ – 1})^2=4^2\) \(\Rightarrow (a^2 + a^{-2} +2)=16\) \(\Rightarrow a^2 + a^{-2}=14\) and now squarring both side again………….

can you finish the problem……..

Squarring both sides of \(a^2 + a^{-2}=14\) \(\Rightarrow (a^2 + a^{-2})^2=(14)^2\) \(\Rightarrow a^4 + a^{-4} +2=196\) \(\Rightarrow a^4 + a^{-4}=194\)

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