If two curves ${y = ax^3 + \sqrt{bx}}$ and ${y = \ln(px^2)}$ intersect at the points where ${x = 1}$

Question

If two curves ${y = ax^3 + \sqrt{bx}}$ and ${y = \ln(px^2)}$ intersect at the points where ${x = 1}$, ${x = 2}$ and ${x = 4}$, find the values of ${a}$, ${b}$ and ${p}$, correct to $2$ decimal places. [4]

Accepted Answer

$a=-0.01$, $b=12.65$, $p=34.63$

2013 TJC P1 Q1

2013 TJC P1 Q1

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