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Black_prince [1.1K]
3 years ago
8

Rationalize the denominator of the following expression and simplify:

Mathematics
1 answer:
Mama L [17]3 years ago
4 0
To "rationalize the denominator" is another way to say, getting rid of that pesky radical at the bottom.

we'll simply start by multiplying top and bottom by the "conjugate" of the denominator, recall difference of squares, anyhow, let's do so

\bf \cfrac{6+\sqrt{2}}{5-\sqrt{2}}\cdot \cfrac{5+\sqrt{2}}{5+\sqrt{2}}\implies \cfrac{(6+\sqrt{2})(5+\sqrt{2})}{(5-\sqrt{2})(5+\sqrt{2})}\implies \cfrac{(6+\sqrt{2})(5+\sqrt{2})}{5^2-(\sqrt{2})^2}
\\\\\\
\cfrac{30+6\sqrt{2}+5\sqrt{2}+(\sqrt{2})^2}{25-2}\implies \cfrac{30+11\sqrt{2}+2}{23}\implies \cfrac{32+11\sqrt{2}}{23}
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The inequality that you have is 5^{n}>2^{2n+1}+100,\,n>4. You can use mathematical induction as follows:

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Now suppose that the inequality holds for n=k and let's proof that the same holds for n=k+1. In fact,

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3 years ago
Find each product by distributing.<br> (2a - 5)(a? – 2a + 1)
Westkost [7]

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Step-by-step explanation:

Given equation as

(2a -5) (a² -2a +1) = 0

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Or, (2a - 5) (a - 1) (a - 1) = 0

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Answer

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