<    1      2      3      4    >

---

Equation x² = 2^x

For the equation x² = 2^x we have three solutions, namely x = 2, x = 4 and x = −0,7667…. Let's do something different, and take x→∞. Then you can write

∞² = 2^∞     ⇒     ∞ = ∞     ⇒     0 = 0          

That seems like a good answer, but something's not right here.

 

---

Explanation

So far, the solutions have been

2² = 2²     ⇒     4 = 4     ⇒     0 = 0

4² = 2⁴     ⇒     16 = 16     ⇒     0 = 0

(−0,7667)² = 2^−0,7667     ⇒     0,587... = 0,587...     ⇒     0 = 0

With infinity it looks different, because

∞² = 2^∞     ⇒     ∞ = ∞     ⇒     ∞ − ∞ = ?

for infinity minus infinity is indefinite. Infinity is not a number with a certain value. So it remains with three solutions.

 

---

Deutsch   Español   Français   Nederlands   中文   Русский