Question

answer it in a 4 marker way.. i mean step by step not direct..​

Answer 1

Answer:

√5+√3/√5-√3×√5+√3/√5+√3

=(√5+√3)²/(√5)²-(√3)²

=(√5)²+(√3)²+2(√5)(√3)/5-3

5+3+2√15/2

=8+2√15/2

Answer 2

Step-by-step explanation:

$\frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \\ \\ \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \\ \\ = \frac{( \sqrt{5} + \sqrt{3} ) ^{2} }{( \sqrt{5}) ^{2} - ( \sqrt{3}) ^{2} } \\ \\ = \frac{( \sqrt{5} )^{2} + ( \sqrt{3}) ^{2} + 2 \times \sqrt{5} \times \sqrt{3} }{5 - 3} \\ \\ = \frac{5 + 3 + 2 \sqrt{15} }{2} \\ \\ = \frac{8 + 2 \sqrt{15} }{2} \\ \\ = \frac{ \cancel2(4 + \sqrt{15} )}{ \cancel2} \\ \\ = 4 + \sqrt{15} \\ \\ \\ a + b \sqrt{5} \\ = 4 + \sqrt{3} \times \sqrt{5} \\ \\ a = 4 \\ \\ b = \sqrt{3}$