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CAT Formulas
Logarithms, Surds and Indices
Deciml into fraction
Formula Video
If $$x = 9 + 4\sqrt{5}$$, what is $$x + \frac{1}{x}$$
17.83
18.45
18.00
None of these
$$x = 9 + 4\sqrt{5}$$. So, $$\frac{1}{x}$$ = $$9 - 4\sqrt{5}$$. So, $$x+ \frac{1}{x}$$ = 18
$$ \frac{1}{{3-2}\sqrt{2}}$$ - $$ \frac{1}{{3+2}\sqrt{2}}$$ = $$2^x$$. Find x?
3/2
5/2
3
7/2
$$\frac{1}{3-2\sqrt{2}}-\frac{1}{3+2\sqrt{2}} = \frac{3+2\sqrt{2}-3+2\sqrt{2}}{3^2-(2\sqrt{2})^2} = 4\sqrt{2}/1 = 2^{5/2}$$. Hence x=5/2.
If $$ x=\sqrt{17}-\sqrt{13}$$, what is $$ \frac{30-\sqrt{884}}{\sqrt{17}+\sqrt{13}}$$?
$$\frac{x^2}{x-1}$$
$$\frac{x^3}{x-1}$$
$$x^3$$
$$\frac{x^3}{4}$$
$$\frac{30-\sqrt{884}}{\sqrt{17}+\sqrt{13}} = \frac{(\sqrt{17}-\sqrt{13})^2}{\sqrt{17}+\sqrt{13}} = \frac{(\sqrt{17}-\sqrt{13})^3}{(\sqrt{17}+\sqrt{13})(\sqrt{17}-\sqrt{13})}=\frac{x^3}{17-13} = \frac{x^3}{4}$$.
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Other Logarithms, Surds and Indices Formulas
Properties of logarithm
Logarithmic Inequality
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