यदि `1/(root(3)(4)+root(3)(2)+1)=aroot(3)(4)+broot(3)(2)+c` और `a,b,c` परिमेय संख्याऐं है तो `a+b+c` किसके बराबर है

Options

A. 0
B. 1
C. 2
D. 3

Answer

A

Explanation

`1/(root(3)(4)+root(3)(2+1))=aroot(3)(4)+broot(3)(2)+c`
`implies 1/(root(3)(4)+root(3)(2)+1)=1/((2^(1/3))^(2)+2^(1/3)+(1)^(2))`
`implies ( :. A^(3)-B^(3)=(A-B)(A^(2)+AB+B^(2))`
`:.` Put `A=2^(1/3), B=1`
`=((2^(1/3)-1))/((2^(1//3)-1)((2^(1/3))^(2)+2^(1/3)+(1)^(2)))`
`=((2^(1/3)-1))/((2^(1/3))^(3)-(1)^(3))=(2^(1/3)-1)`
`2^(1/3)-1=a(2^(2/3))+b(2)^(1/3)+c`
(comparing the terms)
`a=0`
`b=1`
`c=-1`
`:. a+b+c=0+1-1=0`