If and are the roots of 7x^2-3x-2=0, then the value of 1-^2+1-^2 is equal to:

Question

If $\alpha$ and $\beta$ are the roots of $7x^2-3x-2=0$, then the value of $\dfrac\alpha{1-\alpha^2}+\dfrac\beta{1-\beta^2}$ is equal to:

Accepted Answer

$\alpha+\beta=\dfrac37$, $\alpha\beta=-\dfrac27$.

$$\frac\alpha{1-\alpha^2}+\frac\beta{1-\beta^2}=\frac{(\alpha+\beta)-\alpha\beta(\alpha+\beta)}{1-(\alpha+\beta)^2+2\alpha\beta+(\alpha\beta)^2}=\frac{\frac37+\frac27\cdot\frac37}{1-\frac9{49}-\frac47+\frac4{49}}=\frac{27}{16}.$$

Solutions · 1