AM-84

Line meeting a curve

A Math · Secondary 3 · Hard · Line meeting a curve

The graphs of

y=3x^3

and

y^2=6x

intersect at a point where

x>0

. Find the coordinates of this point.

$\big((\tfrac{2}{3})^{1/5},\;3(\tfrac{2}{3})^{3/5}\big)$
$\big((\tfrac{2}{3})^{1/5},\;6(\tfrac{2}{3})^{3/5}\big)$
$\big((\tfrac{2}{3})^{1/6},\;3(\tfrac{2}{3})^{1/2}\big)$
$(0,0)$

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