If `alpha, beta` are roots of `x^(2)-2x-1=0`, then value of `5alpha^(4)+12beta^(3)` is

Options

A. 153
B. 169
C. 183
D. None of these

Answer

C

Explanation

`2x^(3)y dy+(1-y^(2))(x^(2)y^(2)+y^(2)-1)dx=0`
`implies ((2y)/(1-y^(2)))(dy)/(dx)+(x^(2)y^(2)+y^(2)-1)/(x^(3))=0`
`implies ((2y)/(1-y^(2)))(dy)/(dx)+(y^(2))/(x)=(1-y^(2))/(x^(3))`
`implies (2y)/((1-y^(2))^(2))(dy)/(dx)+(1)/(x)((y^(2))/(1-y^(2)))=(1)/(x^(3))`
`(dt)/(dx)+(1)/(x)t=(1)/(x^(3))("where " t = (y^(2))/(1-y^(2)))`
`x(dt)/(dx)+t=(1)/(x^(2))implies (d)/(dx)(tx)=(1)/(x^(2))`
`tx=-(1)/(x)+C`
`(x^(2)y^(2))/(1-y^(2))=(Cx-1)impliesx^(2)y^(2)=(Cx-1)(1-y^(2))`