Equation x² = 2˟

< 1 2 3 4 >

For the equation x² = 2^x there are two simple solutions, those are is x = 2 and x = 4. There is another solution, but it is not easy to guess.

With a bit of dexterity, you'll find the value x = −0,7667…. on a calculator, because

2^−0,7667 = 0,587… and (−0,7667)² = 0,587…

where this answer is accurate to three decimal places. The three intersections can be seen in the graph.

I don't know how you calculate this. So let's leave it here. And now, of course, the question: Are there any other solutions?

You can see that the functions y₁ = x² and y₂ = 2^x have three points of intersection

x = −0,766666469, x = 2 and x = 4