Question

find the values of a and b if √2+√3/3√2-2√3 = a+b√6
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Answer 1

Question:

$\sf Find \ the \ values \ of \ a \ and \ b \ if \ \ \dfrac{\sqrt{2} + \sqrt{3}}{3\sqrt{2} - 2\sqrt{3}} = a + b\sqrt{6}$

Solution:

LHS;

$\Longrightarrow \sf \dfrac{\sqrt{2} + \sqrt{3}}{3\sqrt{2} - 2\sqrt{3}} \\ \\ \\ \\\Longrightarrow \sf \dfrac{\sqrt{2} + \sqrt{3}}{3\sqrt{2} - 2\sqrt{3}} \times \dfrac{3\sqrt{2} + 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} \\ \\ \\ \\\Longrightarrow \sf \dfrac{\left(\sqrt{2} + \sqrt{3}\right) \left( 3\sqrt{2} + 2\sqrt{3}\right)}{\left(3\sqrt{2} - 2\sqrt{3}\right) \left(3\sqrt{2} + 2\sqrt{3}\right)}\\ \\ \\ \\\Longrightarrow \sf \dfrac{3(2) + 2\sqrt{6} + 3\sqrt{6} + 2(3)}{(3\sqrt{2})^2 - (2\sqrt{3})^2}$

$\Longrightarrow \sf \dfrac{6 + 5\sqrt{6} + 6}{9(2) - 4(3)} \\ \\ \\ \\\Longrightarrow \sf \dfrac{12 + 5\sqrt{6}}{18 - 12} \\ \\ \\ \\\Longrightarrow \sf \dfrac{12 + 5\sqrt{6}}{6} \\ \\ \\ \\\Longrightarrow \sf \dfrac{12}{6} + \dfrac{5\sqrt{6}}{6} \\ \\ \\ \\\Longrightarrow \sf 2 + \dfrac{5\sqrt{6}}{6}$

ATQ, This is equal to a + b√6.

$\Longrightarrow \sf 2 + \dfrac{5\sqrt{6}}{6} = a + b\sqrt{6}$

∴ a = 2

∴ b = 5/6

Answer 2

Answer:

The answer is 2,-5/6

Explanation:

a=2,b=-5/6

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