यदि `x` एक परिमेय संख्या है और `((x+1)^(3)-(x-1)^(3))/((x+1)^(2)-(x-1)^(2))=2` है तो `x` के अंश तथा हर का योग ज्ञात करें।

Options

A. 3
B. 4
C. 5
D. 7

Answer

B

Explanation

`((x+1)^(3)-(x-1)^(3))/((x+1)^(2)-(x-1)^(2))=2`
`implies A^(3)-B^(3)+(A-B)(A^(2)+AB+B^(2))`
`A^(2)-B^(2)=(A-B)(A+B)`
`implies ((x+1-x+1)((x+1)^(2)+(x-1)(x+1)+(x-1)^(2)))/((x+1-x+1)(x+1+x-1))`
`=2`
`implies ((x^(2)+1+3x+x^(2)-1+x^(2)+1-2x))/((2x))=2`
`implies (3x^(2)+1)/(2x)=`
`implies 3x^(2)+1=4x`
`3x^(2)-4x+1=0`
`3x^(2)-3x-x+1=0`
`3x(x-1)-1(x-1)=0`
`(3x-1)(x-1)=0`
`implies 3x-1=0`
`x=1/3`
`implies x-1=0`
for `x=1=1/1`
By adding numinator and denominator
`1+1=2`
No option is satisfied
`:. x=1/3`
`1+3=4`