Find the values of a and b if 7 - 3-53 - -5 - 7 - 3-53 - -5 - a - -5 b

7 + 3√(5)3 + √(5) 7 3√(5)3 √(5) = a + √(5) b 7 + 3√(5)3 + √(5)×3 √(5)3 √(5) 7 3√(5)3 √(5)×3 + √(5)3 + √(5) = a + √(5) b ( 7 + 3√( ...

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Componendo and Dividendo

Find the valu...

Question

Find the values of $a$ and $b$ if
$\frac{7 + 3 \sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3 \sqrt{5}}{3 - \sqrt{5}} = a + \sqrt{5} b$

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Find the values of a and b if 7+3√5/3+√5 - 7-3√5/3-√5 = a+b√5

\frac{7 + 3 \sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3 \sqrt{5}}{3 - \sqrt{5}}

a + b \sqrt{5}

(i) \frac{5 + 2 \sqrt{3}}{7 + 4 \sqrt{3}} = a - 6 \sqrt{3}

(i i) \frac{3 - \sqrt{5}}{3 + 2 \sqrt{5}} = a \sqrt{5} - \frac{19}{11}

(i i i) \frac{\sqrt{2} + \sqrt{3}}{3 \sqrt{2} - 2 \sqrt{3}} = 2 - b \sqrt{6}

(i v) \frac{7 + \sqrt{5}}{7 - \sqrt{5}} - \frac{7 - \sqrt{5}}{7 + \sqrt{5}} = a + \frac{7}{11} \sqrt{5} b

(i) \frac{5 + 2 \sqrt{3}}{7 + 4 \sqrt{3}} = a - 6 \sqrt{3}

(i i) \frac{3 - \sqrt{5}}{3 + 2 \sqrt{5}} = a \sqrt{5} - \frac{19}{11}

(i i i) \frac{\sqrt{2} + \sqrt{3}}{3 \sqrt{2} - 2 \sqrt{3}} = 2 - b \sqrt{6}

(i v) \frac{7 + \sqrt{5}}{7 - \sqrt{5}} - \frac{7 - \sqrt{5}}{7 + \sqrt{5}} = a + \frac{7}{11} \sqrt{5} b

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

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