1.

Sum of the series `P=(1)/(2sqrt(1)+sqrt(2))+(1)/(3sqrt(2)+2sqrt(3))+.........+(1)/(100sqrt(99)+99sqrt(100))` isA. `(1)/(10)`B. `(3)/(10)`C. `(9)/(10)`D. `(1)/(2)`

Answer» Correct Answer - B
Put `y=x+(3+5)/(2)=x+4`
The equation becomes
`(y-1)^(4)+(y+1)^(4)=16`
`implies2{y^(4)+6y^(2)+1}=16 " "implies" "y^(4)+6y^(2)-7=0`
`implies (y^(2)+7)(y^(2)-1)=0" "implies " "y^(2)=-7" or "y^(2)=1`
`implies y=pmsqrt(7i)" or "y= pm1 " "implies " "x=-4pmsqrt(7i) " or " x=-4pm1=-5" or "-3`.
Thus, the given equation has two real roots.


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