1.

Sum of the series P=(1)/(2sqrt(1)+sqrt(2))+(1)/(3sqrt(2)+2sqrt(3))+.........+(1)/(100sqrt(99)+99sqrt(100)) is

Answer»

`(1)/(10)`
`(3)/(10)`
`(9)/(10)`
`(1)/(2)`

Solution :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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