Question

(7+3 root 5 / 2+root 5) - (7-3root5/2-root5) = a+b Find the value of a and b

Answer 1

Answer:

\frac{7 + 3 \sqrt{5} }{3 + \sqrt{5} } - \frac{7 - 3 \sqrt{5} }{3 - \sqrt{5} } = a + b \sqrt{5} \\ or. \: \frac{(7 + 3 \sqrt{5})(3 - \sqrt{5}) - (7 - 3 \sqrt{5} )(3 + \sqrt{5} ) }{(3 + \sqrt{5})(3 - \sqrt{5} )} = a + b \sqrt{5} \\ or. \: \frac{(21 - 7 \sqrt{5} + 9 \sqrt{5} - 15) - (21 - 9 \sqrt{5} + 7 \sqrt{5} - 15) }{ {3}^{2} - {( \sqrt{5} )}^{2} } = a + b \sqrt{5} \\ or. \: \frac{6 + 2 \sqrt{5} - 6 + 2 \sqrt{5} }{9 - 5} = a + b \sqrt{5} \\ or. \: \frac{4 \sqrt{5} }{4} = a + b \sqrt{5} \\ or. \: \sqrt{5} = a + b \sqrt{5} \\ \\ so \: a = 0....and \: \: b = 1

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