1.

`(x^(4)+3x^(3)+5x^(2)+3x+1)/(x^(4)+1)` का मान ज्ञात करें।A. `43/23`B. `47/21`C. `41/23`D. `45/21`

Answer» Correct Answer - A
`x+1/x=5, x^(2)+1/(x^(2))+2=25`
`x^(2)+1/(x^(2))=23`
Now
`(x^(4)+3x^(3)+5x^(2)+3x+1)/(x^(4)+1)`
divided by `x^(2)`
`((x^(4))/(x^(2))+(3x^(3))/(x^(2))+(5x^(2))/(x^(2))+(3x)/(x^(2))+1/(x^(2)))/((x^(1))/(x^(2))+1/(x^(2)))`
`=(x^(2)+3x+5+3x+1/(x^(2)))/(x^(2)+1/(x^(2))`
`=(x^(2)+1/(x^(2))+3(x+1/x)+5)/(x^(2)+1/(x^(2)))`
`=(23+3(5)+5)/23=43/23`


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