Question

7y^2-y-1/2=0
y=? smaller value
y=? larger value

Answer 1

\[7y^2 - y - (1/2) = 0\]

\[14y^2 - 2y - 1 = 0\]

\[y= \left[2 \pm \sqrt{4 - 4(14)(-1)}\right]\left(\frac{1}{28}\right)\]
\[y= \left[2 \pm \sqrt{60}\right]\left(\frac{1}{28}\right)\]
\[y= \left[2 \pm 2\sqrt{15}\right]\left(\frac{1}{28}\right)\]
\[y= \left[1 \pm \sqrt{15}\right]\left(\frac{1}{14}\right)\]
so \[y = \frac{1}{14} + \frac{\sqrt{15}}{14}\] (the larger one)
and \[y = \frac{1}{14} - \frac{\sqrt{15}}{14}\] (the smaller one)