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Sunday Afternoon Maths LV

 Posted on 2016-10-16 

Powerful quadratics

Source: nrich
Find all real solutions to
$$(x^2-7x+11)^{(x^2-11x+30)}=1.$$

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Two tangents

Source: Reddit
Find a line which is tangent to the curve \(y=x^4-4x^3\) at 2 points.

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Blackboard sums

The numbers 1 to 20 are written on a blackboard. Each turn, you may erase two numbers, \(a\) and \(b\) and write the sum \(a+b\) in their place. You continue until only one number remains.
What is the largest number you can make?

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Tags: numbers
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