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If $\dfrac{a^2 -1}a = 5$ then find the value of $\dfrac{a^6 - 1}{a^3}$.

Théophile
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Anandesh Sharma
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1 Answers1

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Hint: Contest math loves the expressions $a\pm\frac 1a$. You should recognize your left side as one of these. Powers of them are quite simple because terms combine. You are looking for $a^3-\frac 1{a^3}$. How can you get something that looks somewhat like that?

Ross Millikan
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  • Solved! Using this expression. Thanks! – Anandesh Sharma Aug 25 '18 at 05:20
  • Another case if you see a polynomial where the coefficients are symmetric, like $ax^4+bx^3+cx^2+bx+a$ you should divide it by $x^2,$ define $y=x+\frac 1x$ and write it as a polynomial in $y$. You have a quadratic instead of a quartic then. – Ross Millikan Aug 25 '18 at 14:09