a और b के मान ज्ञात कीजिए , यदि
(i) `(sqrt(3) + 1 )/(sqrt(3) - 1) = a+bsqrt(3)`, (ii) `(5+2sqrt(3))/(5-2sqrt(3)) = a + b sqrt(3)`

Explanation

(i) `a+bsqrt(3) = (sqrt(3) + 1)/(sqrt(3) - 1) = (sqrt(3) + 1)/(sqrt(3) - 1 ) xx (sqrt(3) + 1)/(sqrt(3) + 1)`
`= (3 + 1 + 2sqrt(3))/((sqrt(3))^(2) - (1)^(2)) = ( 4 + 2sqrt(3))/(3-1) = (2(2+sqrt(3)))/(2) = 2 + 1sqrt(3)`
तुलना करने पर
`a = 2 , b = 1`
(ii) `a+bsqrt(3) = (5+ 2sqrt(3))/(5-2sqrt(3)) = (5+2sqrt(3))/(5-2sqrt(3)) xx (5+2sqrt(3))/(5+2sqrt(3))`
`= ((5)^(2) +(2sqrt(3))^(2) + 2(5) (2sqrt(3)))/((5)^(2) - (2sqrt(3))^(2))`
`= (25 + 12 + 20sqrt(3))/(25-12)`
`= (37 + 20sqrt(3))/(13) = (37)/(13) + (20sqrt(3))/(13)`
तुलना करने पर
`a = (37)/(13) , b = (20)/(13)`