Question

the steps with the answer

Answer 1

$\dfrac{7 + 3\sqrt{5}}{3 + \sqrt{5}} - \dfrac{7 - 3\sqrt{5}}{3 - \sqrt{5}} = a + \sqrt{5b}$

$\dfrac{(7 + 3\sqrt{5}) (3 - \sqrt{5})- (7 - 3\sqrt{5} ) ({3 + \sqrt{5}}) } {(3 + \sqrt{5})(3 - \sqrt{5}) } = a + \sqrt{5b}$

$\dfrac{ [ (7)(3) - 7(\sqrt{5}) + 9(\sqrt{5}) - 3(5) ] - [ (7)(3) + 7(\sqrt{5}) - 9(\sqrt{5}) - 3(5) ] } {3^2 - 5 } = a + \sqrt{5b}$

$\dfrac{ [6 + 2(\sqrt{5}) ] - [ 6 -2 (\sqrt{5}) ] } {4 } = a + \sqrt{5b}$

$\dfrac{ 6 + 2(\sqrt{5}) - 6 +2(\sqrt{5}) } {4 } = a + \sqrt{5b}$

$\dfrac{ 4(\sqrt{5}) } {4 } = a + \sqrt{5b}$

$\sqrt{5} = a + \sqrt{5b}$

$a + \sqrt{5b} = \sqrt{5}$

Therefore a = 0 and b = 1

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Answer : a = 0, b = 1