Question

please solve this. Value of a and b

Answer 1

Hi...✌

Here is your answer...☺

(iii) : On rationalising LHS

we get

LHS =
$\frac{3}{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} } { \sqrt{3} + \sqrt{2} } \\ \\ = \frac{3 \sqrt{3} + 3 \sqrt{2} }{( \sqrt{3} )^{2} - ( \sqrt{2})^{2} } \\ \\ = \frac{3 \sqrt{3} + 3 \sqrt{2} }{3 - 2} = 3 \sqrt{3} + 3 \sqrt{2}$
Now by comparing LHS and RHS

3√3 + 3√2 = a√3-b√2

we get , a = 3 , b = -3

(iv) : On rationalising LHS

LHS =

$\frac{5 + 3 \sqrt{2} }{5 - 3 \sqrt{2} } \times \frac{5 + 3 \sqrt{2} }{5 + 3 \sqrt{2} } \\ \\ = \frac{ {5^{2} + (3 \sqrt{2} )}^{2} + 30 \sqrt{2} }{ {5}^{2} - ({3 \sqrt{2} })^{2} } \\ \\ = \frac{25 + 18 +30 \sqrt{2} }{25 - 18} \\ \\ = \frac{43 + 30 \sqrt{2} }{7} \\ \\ = \frac{43}{7} + \frac{30 \sqrt{2} }{7}$

By comparing LHS and RHS

43/7 +(30/7)√2 = a + b√2

=> a = 43/7 and b = 30/7

Thank you ⭐