1.

If `x+y=t-(1)/(t),x^(2)+y^(2)=t^(2)+(1)/(t^(2))`, what is `(dy)/(dx)` equal to?A. `(1)/(x)`B. `-(1)/(x)`C. `(1)/(x^(2))`D. `-(1)/(x^(2))`

Answer» Correct Answer - C
Given that `x+y=t-(1)/(t) and x^(2)+y^(2)=t^(2)+(1)/(t^(2))`
`therefore" "(x+y)^(2)=x^(2)+y^(2)+2xy`
`rArr" "(t-(1)/(t))^(2)=(t^(2)+(1)/(t^(2)))+2xy`
`-2=2xyrArrxy=-1`
`(x-y)^(2)=(x+y)^(2)-4xy`
`=(t-(1)/(t))^(2)-4xx-1=t^(2)+(1)/(t^(2))-2+4=(t+(1)/(t))^(2)`
`x-y=t+(1)/(t)`
`rArr" "x=t, u=-(1)/(t)`
`xy=-1`
`rArr" "x(dy)/(dx)+y=0`
`rArr" "(dy)/(dx)=-(y)/(x)=(1)/(t^(2))=(1)/(x^(2))`


Discussion

No Comment Found

Related InterviewSolutions