Try this beautiful problem from Algebra based on quadratic equation
Suppose that the number \(a\) satisfies the equation \(4 = a + a^{ - 1}\). What is the value of \(a^{4} + a^{ - 4}\)?
Algebra
Linear equation
multiplication
Answer: \(194\)
AMC-10A (2007) Problem 20
Pre College Mathematics
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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