Question

Let $\alpha ,\beta$ be the roots of the equation $x^2+x-1=0$ then find the value of ${\alpha }^2+{\beta }^2$.

Answer 1

Given $\alpha ,\beta$ are roots of the equation

$x^2+x-1=0$

Then from the relation between roots and coefficients we get,

$\alpha +\beta =-1$ ………$\left(1\right)$

$\alpha \beta =-1$ ………..$\left(2\right)$

Now, ${\alpha }^2+{\beta }^2$

$=(\alpha +\beta {)}^2-2\alpha \beta$

$=(-1{)}^2+2$

$=1+2$

$=3$.