Question

Find the value of a and b, if a + b√2 =
3+ √2
3− √2

Answer 1

Answer:

$\tt \huge a = \frac{11}{7} \: \: \: and \: \: \: b = \frac{6}{7}$

Appropriate question:-

• Find the value of a and b, if a + b√2 = 3+√2 / 3-√2

Solution:-

First rationalise them,

$\to\tt \frac{3 + \sqrt{2} }{3 - \sqrt{2} } \times \frac{3 + \sqrt{2} }{3 + \sqrt{2} } \\ \\ \to \tt \frac{( {3 + \sqrt{2}) }^{2} }{( {3})^{2} - { (\sqrt{2}) }^{2} } \\ \\ \tt \to \frac{ {3}^{2} + { (\sqrt{2} )}^{2} + 2 \times 3 \times \sqrt{2} }{9 - 2} \\ \\ \tt \to \frac{9 + 2 + 6 \sqrt{2} }{7} \\ \\ \tt \to \frac{11 + 6 \sqrt{2} }{7}$

So, a+b√2 = 11+6√2 /7

Hence value of :-

$\tt \huge a = \frac{11}{7}$

$\tt \huge b = \frac{6}{7}$

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