Question

(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))=a+bsqrt(15)

Answer 1

$Answer :\\ \\ Now, \\ \\ \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \\ \\ = \frac{( \sqrt{5} + \sqrt{3} ) }{( \sqrt{5} - \sqrt{3} )} \times \frac{( \sqrt{5} + \sqrt{3} )}{ (\sqrt{5} + \sqrt{3} )}, \\ by \: \: rationalising \: \: the \: \: denominator \\ by \: \: multiplying \: \: both \: \: the \\ numerator \: \: and \: \: denominator \\ by \: \: ( \sqrt{5} + \sqrt{3} ).\\ \\ = \frac{5 + 2 \sqrt{15} + 3 }{5 - 3} \\ \\ = \frac{8 + 2 \sqrt{15} }{2} \\ \\ = 4 + \sqrt{15} \\ \\Given \: \: that, \\ \\ 4 + \sqrt{15} = a + b \sqrt{15} \\ \\ Comparing \: \: both \: \: sides, \: we \: \: get \\ \\ a = 4 \: \: and \: \: b = 1$

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Answer 2

(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))=a+bsqrt(15)

a=4 ;  b=1

Explanation:

Assumption: The question should be:

√5 +√3  =  a + √15 b

√5 - √3

Consider the left hand side (LHS) only

=   √5 +√3  × 1

     √5−√3

=  √5 + √3    × √5 + √3

    √5 −√3          √5 + √3

=   (√5+√3)  (√5+√3)

                5−3

=       5+2√3×5+3

                  2

=         8    + 2√15

            2          2

=         4 + √15

putting it all together

      4 + √15  = a + √15   b

thus a = 4 ; b = 1

Answer is a = 4 ; b = 1

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