1.

यदि `xgt1` और `x+1/x=2 1/12` है तो `x^(4)-1/(x^(4))` का मान ज्ञात करें।A. `58975/20736`B. `59825/20736`C. `57985/20736`D. `57895/20736`

Answer» Correct Answer - A
`x+1/x=2 1/12=25/12`
`x^(2)+1/(x^(2))+2=675/144`
`x^(2)+1/(x^(2))=625/144=2`
`x^(2)+1/(x^(2))=(625-288)/144`
`x^(2)+1/(x^(2))=337/144-2`
`(x-1/x)^(2)=(337-288)/144=49/144`
`x-1/x=7/12`
`:. (x+1/x)(x-1/x)=25/12xx7/12=175/144`
`:. (x^(2)-1/(x^(2))=175/144`
`:. x^(4)=(x^(2)+1/(x^(2)))(x^(2)-1/(x^(2)))`
`=175/144xx337/144=58975/20736`


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