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Show that y=x^3 and 6y=7-x^2 intersect o...

Show that `y=x^3` and `6y=7-x^2` intersect orthogonally:

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`y=x^{3} ldots(1)`
`6 y=7-x^{2} ldots(2)`
From `(1)` and `(2)` we get
`6 x^{3}=7-x^{2}`
`Rightarrow 6 x^{3}+x^{2}-7=0`
`x=1` satisfies this
Dividing this by `x-1`, we get
`6 x^{2}+7 x+7=0`
...
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