Question

9. Find the values of a and b
7+3√5/ 3+√5 - 7-3√5/ 3-√5 = a + b√5
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Answer 1

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

$\frac{(7 + 3 \sqrt{5)}(3 - \sqrt{5)} - (7 - 3 \sqrt{5)} (3 + \sqrt{5)} }{(3 + \sqrt{5)} (3 - \sqrt{5)} }$

$\frac{21 - 7 \sqrt{5} + 9 \sqrt{5} - 15 - (21 + 7 \sqrt{5} - 9 \sqrt{5} - 15) }{9 - 5}$

$\frac{ - 14 \sqrt{5} + 18 \sqrt{5} }{4}$

$- 7 \sqrt{5 } + \frac{9}{2} \sqrt{5}$

now compare it with RHS

so,

a= -7√5

and b= 9/2