Question

If α β are roots of y^2-2y-7=0. Then find the α^2+β^2 and α^3+β^3.

Answer 1

$y^2-2y-7=0$ which roots are α or β

Know that :

$\alpha +\beta =2$

$\alpha \beta =-7$

Also know that :

$(a+b)^2-2ab=a^2+b^2$

$(a+b)^3-3ab(a+b)=a^3+b^3$

∴ $\alpha ^2+\beta ^2=2^2-2\times (-7)=18$

∴ $\alpha ^3+\beta ^3=2^3-3\times (-7) \times 2=8+42=50$