Question

Find the value of a and b if 5+3√2/5-2√2 = a+b√2​

Answer 1

Answer:

Answer

__________

__________

Step-by-step explanation:

$\longrightarrow$$\\ \red\bigstar\tt\: \dfrac{5+3\sqrt2}{5-2\sqrt2}$

$\longrightarrow$$\\ \red\bigstar\tt\: \dfrac{5+3\sqrt2}{5-2\sqrt2} \times\dfrac{5+2\sqrt2}{5+2\sqrt2}$

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

$\frac{5(5 + 2 \sqrt{2} ) + 3 \sqrt{2}(5 + 2 \sqrt{2} ) }{5 - 8}$

$\frac{25 + 10 \sqrt{2} + 15 \sqrt{2} + 12}{ - 3}$

$\frac{37 + 25 \sqrt{2} }{ - 3}$

Answer 2

Answer:

$\frac{5 + 3 \sqrt{2} }{5 - 2 \sqrt{2} } = a + b \sqrt{2} \\ \frac{5 + 3 \sqrt{2} }{5 - 2 \sqrt{2} } \times \frac{5 + 2 \sqrt{2} }{5 + 2 \sqrt{2} } = a + b \sqrt{2} \\ \frac{25 + 10 \sqrt{2 } + 15 \sqrt{2 +} + 12}{25 - 8} = a + b \sqrt{2} \\ \frac{37 + 25 \sqrt{2} }{17} = a + b \sqrt{2} \\ \\ a = \frac{37}{17} \: \:,. b = \frac{25}{17}$

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