Question

Find a and b
(5+3√2)/(5-3√2) = a+b√2

Don't give any other answers

Answer 1

Answer:

We rationalize the denominator

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Answer 2

$\bold \red \star \: \underline{Given:-}$

$\frac{5 + 3 \sqrt{2} }{5 - 3 \sqrt{2} } = a + b \sqrt{2} .$

$\rule{200}2$

$\\ \\ \bold \red \star \: \underline{Solution:-}$

$\tt{Taking \: \red{LHS}.}$

$\frac{5 + 3 \sqrt{2} }{5 - 3 \sqrt{2} }$

$\tt{Rationalize \: the \: \red{ denominator}.}$

$\frac{5 + 3 \sqrt{2} }{5 - 3 \sqrt{2} } \times \frac{5 + 3 \sqrt{2} }{5 + 3 \sqrt{2 } } \\ \\ \frac{ {(5 + 3 \sqrt{2} ) }^{2} }{ {(5)}^{2} - {(3 \sqrt{2}) }^{2} }$

$\\ \frac{25 + 18 + 30 \sqrt{2} }{25 - 18}$

$\frac{43 + 30 \sqrt{2} }{7}$

$Or, \\ \\ \: \: \: \: \: \: \: \: \red{a} = \frac{43}{7} \: \: \: \: \: \: \: \: \: \: \: \: \: \red{b }= \frac{30 \sqrt{2} }{7} .$