Can any kind soul help me in the below?

Please assist in (b)

a) Factorise t^4 - 16

b) If (x + 2/x)^2 = 36, then what is (x^2 + 2/x^2)^2?

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- Feb 11th 2010, 12:51 AM #1

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- Feb 11th 2010, 01:09 AM #2
Well, a) is easy, if you note that $\displaystyle 16 = 4^2$ (or $\displaystyle 2^4$).

__Second question__: I guess there is another more clever way to do this but I would have solved for $\displaystyle x$ first, then evaluated.

Since $\displaystyle (x + \frac{2}{x})^2 = 36$, we have $\displaystyle x + \frac{2}{x} = 6$, thus $\displaystyle \frac{x^2}{x} + \frac{2}{x} = 6$, therefore $\displaystyle \frac{x^2 + 2}{x} = 6$, so $\displaystyle x^2 + 2 = 6x$, and so, $\displaystyle x^2 - 6x + 2 = 0$.

By means of the quadratic formula (for example), you find that $\displaystyle x$ equals that value and that value, then you substitute your results back into the second equation and evaluate.

Does that make sense ?

- Feb 11th 2010, 01:52 AM #3

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- Feb 11th 2010, 03:43 AM #4

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- Feb 11th 2010, 06:24 AM #5

- Feb 11th 2010, 01:31 PM #6

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