Question

find "a" and "b"
please help ​

Answer 1

Solve the given equation:

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

Rationalize it:

=> $\tt{\frac{3 + \sqrt{2}}{3 - \sqrt{2}} \times \frac{3+\sqrt{2}}{3+\sqrt{2}} }$

=> $\tt{\frac{(3 + \sqrt{2})^{2}}{(3)^{2} - (\sqrt{2})^{2}}}$

=> $\tt{\frac{9 + 6\sqrt{2} + 2}{9 - 2}}$

=> $\tt{\frac{11 + 6\sqrt{2}}{7}}$

Equate this to the RHS:

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

Thus, we get:

a = 11/7

b = 6/7

Answer 2

Solutions:

(3 + √2)/(3 - √2) = a + b√2

(3 + √2)/(3 - √2) × (3 + √2)/(3 + √2)

(3 + √2)²/(3)² - (√2)²

9 + 6√2 + 2 / 9 - 2

11 + 6√2 / 7 = a + b√2

a = 11/7

b = 6/7

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