Math Arguments

Problems, Questions, and Puzzles to spark discussion and argument in the maths classroom.

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Item 1008

GM in the AM on a GOLDEN Friday

For what value(s) of \(x\) is \(x^2+x+1=2x\sqrt{x+1}\)?

There are many ways to solve this. Wolframalpha, DESMOS. or Geogebra will all give an answer but can you decipher the clues in the heading?

Look at the graphs for the equation in Wolfram. The curves appear to be tangent to each other at the point of intersection. Can you show this to be true? or not?


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David Marain
PRE-CALC

Source: David Marain
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