Question

if 3 + 2 root 2 upon 2 minus root 2 is equal to a + b root 2 find the value of a and b

Answer 1

I hope this solution is helpful for you.

Answer 2

$Given \: \frac{(3+2\sqrt{2})}{(2-\sqrt{2})} = a + b\sqrt{2}$

$LHS = \frac{(3+2\sqrt{2})(2+\sqrt{2})}{(2-\sqrt{2})(2+\sqrt{2})}$

$= \frac{ 6+3\sqrt{2} + 4\sqrt{2} +4}{2^{2} - (\sqrt{2})^{2} }\\= \frac{10 + 7\sqrt{2}}{4-2}\\= \frac{10+7\sqrt{2}}{2}$

$= \frac{10}{2} + \frac{7}{2} \sqrt{2}$

$= 5 + \frac{7}{2} \sqrt{2}$

$LHS = RHS$

$5 + \frac{7}{2} \sqrt{2} = a + b \sqrt{2}$

$a = 5 , \: and \: b = \frac{7}{2}$

Therefore.,

$\green { a = 5 , \: and \: b = \frac{7}{2}}$

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