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Let a and b be the solutions to 5x^2 - 11x + 4 = 4x^2 + 11x + 13. Find \frac{1}{a^3} + \frac{1}{b^3}.

 Jan 15, 2024
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Let a and b be the solutions to \(5x^2 - 11x + 4 = 4x^2 + 11x + 13\). Find \(\frac{1}{a^3} + \frac{1}{b^3}\).

 

For this question, I'm just going to solve for a and b, since it is not that hard.

You can use the quadratic formula, which is \(\frac{-b+or-\sqrt{b^2-4ac}}{2a}\). The +or- just stands for plus or minus. Any moderators tell me what the symbol for that is? I kind of forgot. Anyways, by plugging in the formula to the equation, first we got to simplify it.

\(5x^2 - 11x + 4 = 4x^2 + 11x + 13\)

\(x^2 - 22x -9 =0\)

\(x = \sqrt{130}+11,-\sqrt{130}+11\)

You can take it from here.

 

 

PS: I think you made a mistake, this answer looks kinda weird. Maybe it wasn't +11x it was -11x, so it would be a perfect square and easier to solve.

 Jan 15, 2024

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