Given that P = 4 + $\sqrt2$ and that $\frac{P}{Q}$ = a + b$\sqrt c$ where a, b and c are constants, find the values of a, b and c

Given that P = 4 + $\sqrt2$ and that
$\frac{P}{Q}$ = a + b$\sqrt c$ where a, b and c are constants, find the values of a, b and c

Answers

Substitute $\frac{P}{Q}\; = \; \frac{4 +\sqrt2}{2+\sqrt2}$

Then rationalize the denominator by multiplying
numerator by conjugate of

2 + $\sqrt2 \;which\;is\;2\;-\sqrt2$

therefore $\frac{4\;+\sqrt2}{2 + \sqrt2}$ x $\frac{2 - \sqrt2}{2\;-\sqrt2}$

= $\frac{8 - 4\sqrt2\; + 2\sqrt2 \; -2}{4\; -2\sqrt2 \; + 2\sqrt2 - 2}$

= $\frac{6\; -2\sqrt2}{2}$ = 3 - $\sqrt2$

= a + b$\sqrt c$

equating corresponding elements

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johnmulu answered the question on March 8, 2017 at 06:45

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