यदि `(4sqrt(3)+5sqrt(2))/(sqrt(48)+sqrt(18))=a+bsqrt(6)` है तो `a` और `b` का मान क्रमशः क्या होगा?

Options

A. `9/15,-4/15`
B. `3/11,4/33`
C. `9/10,5/2`
D. `3/5,4/15`

Answer

D

Explanation

`(4sqrt(3)+5sqrt(2))/(sqrt(48)+sqrt(18))=a+bsqrt(6)`
`implies(4sqrt(3)+5sqrt(2))/(sqrt(16xx3)+sqrt(9xx2))`
`=(4sqrt(3)+5sqrt(2))/(4sqrt(3)+3sqrt(2))`
`implies (4sqrt(3)+5sqrt(2))/(4sqrt(3)+3sqrt(2))`
`implies (4sqrt(3)+5sqrt(2))/(4sqrt(3)+3sqrt(2))xx(4sqrt(3)-3sqrt(2))/(4sqrt(3)-3sqrt(2))`
`=((4sqrt(3)+5sqrt(2))(4sqrt(3)-3sqrt(2)))/(48-18)`
`=(8sqrt(6)+18)/30=(8sqrt(6))/30+18/30`
`=4/15sqrt(6)`
`:. 3/5+4/15sqrt(6)=a+bsqrt(6)`
By comparing coefficient of rational and irrational parts.
`implies a=3/5 b=4/15`
`(3/5,4/15)`