if a and b are the roots of x²=x+1 then the value of a²/b-b²/a is 
 

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if a and b are the roots of x²=x+1 then the value of a²/b+b²/a is 
$$\begin{gathered} \mathrm{Since} \mathrm{a} \mathrm{and} \mathrm{b} \mathrm{are} \mathrm{the} \mathrm{roots} \mathrm{of} \mathrm{the} \mathrm{equation} {\mathrm{x}}^2-\mathrm{x}-1=0 \\ \mathrm{So}, \mathrm{a}+\mathrm{b}=1 \\ \mathrm{and} \mathrm{ab}=-1 \\ \mathrm{So}, \frac{{\mathrm{a}}^2}{\mathrm{b}}+\frac{{\mathrm{b}}^2}{\mathrm{a}} \\ =\frac{{\mathrm{a}}^3+{\mathrm{b}}^3}{\mathrm{ab}} \\ =\frac{\left(\mathrm{a}+\mathrm{b}\right)\left({\mathrm{a}}^2+{\mathrm{b}}^2-\mathrm{ab}\right)}{\mathrm{ab}} \\ =\frac{\left(\mathrm{a}+\mathrm{b}\right)\left[{\left(\mathrm{a}+\mathrm{b}\right)}^2-2\mathrm{ab}-\mathrm{ab}\right]}{\mathrm{ab}} \\ =\frac{1\left[1-2\left(-1\right)-(-1)\right]}{-1} \\ =-4 \end{gathered}$$