Question

5 Find the value of a & bif: 3:45 = a + bV5​

Answer 1

$\huge\fcolorbox{red}{cyan}{a=7/2\:and\:b=3/2}$

Step-by-step explanation:

$\frac{3 + \sqrt{5} }{3 - \sqrt{5} } \\ = > \bf{lets \: rationalize} \\ = > \frac{3 + \sqrt{5} }{3 - \sqrt{5} } \times \frac{3 + \sqrt{5} }{3 + \sqrt{5} } \\ = > \bf \color{purple}{ \frac{(x + y) {}^{2} = {x}^{2} + {y}^{2} + 2xy}{(x - y)(x + y) = {x}^{2} - {y}^{2} } } \\ = > \frac{(3 {)}^{2} + ( \sqrt{5} ) ^{2} + (2 \times 3 \times \sqrt{5} )}{( {3)}^{2} - ( \sqrt{5 {)}^{2} } } \\ = > \frac{9 + 5 + 6 \sqrt{5} }{9 - 5} \\ = > \frac{14 + 6 \sqrt{5} }{4} \\ = > \frac{14}{4} + \frac{6 \sqrt{5} }{4} \\ = > \frac{7}{2} + \frac{3 \sqrt{5} }{2}$

Thus The Value of a is '7/2' and Value of b is '3/2'