Question

3+√2÷ 3-√2=a+b√2, find a b​

Answer 1

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Answer 2

Answer:

$\frac{11}{7}+\frac{6}{7}\sqrt{2}= a+b\sqrt{2}$

Therefore,

$a = \frac{11}{7},\\b = \frac{6}{7}$

Step-by-step explanation:

$LHS = \frac{3+\sqrt{2}}{3-\sqrt{2}}\\=\frac{(3+\sqrt{2})^{2}}{(3-\sqrt{2})(3+\sqrt{2})}\\=\frac{9+2+6\sqrt{2}}{9-2}\\=\frac{11+6\sqrt{2}}{7}\\=\frac{11}{7}+\frac{6}{7}\sqrt{2}\\=RHS$

/* According to the problem given,

$\frac{11}{7}+\frac{6}{7}\sqrt{2}= a+b\sqrt{2}$

Therefore,

$a = \frac{11}{7},\\b = \frac{6}{7}$

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