AM-1260

Linear–quadratic simultaneous equations

A Math · Secondary 4 · Hard · Linear–quadratic simultaneous equations

The curve

xy - 4x = 6

intersects the line

y = 2x + 1

at points

P

and

Q

. Find the

y

-coordinates of

P

and

Q

.

$\dfrac{5+\sqrt{57}}{2}$ and $\dfrac{5-\sqrt{57}}{2}$
$\dfrac{3+\sqrt{57}}{2}$ and $\dfrac{3-\sqrt{57}}{2}$
$\dfrac{5+\sqrt{33}}{2}$ and $\dfrac{5-\sqrt{33}}{2}$
$\dfrac{3+\sqrt{33}}{2}$ and $\dfrac{3-\sqrt{33}}{2}$

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