How to Solve this Exponential Equation In 1 minute! 25^x+5^x=2 | Math Challenging Problem

In this video, I will be showing you how to solve this nice exponential equation, 25^x+5^x=2. This algebraic problem is part of the math challenging problems so do not ignore. Check out some other way of solving exponential equation.

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[SuperYoonHo]

This was very nice! let 5^x=y we get y^2+y=2

[nelt]

And we can solve it by (5^x)² + (5^x) - 2 = 0, lets say t = 5^x for comfort.
t^2 + t - 2 = 0, D = 1^2 - 4 * (-2) * 1 = 9, t = (-1 + 3) / 2 = 1(we exclude negative root), so t = 5^x = 1, and x = log5(1)

[ytlongbeach]

x=0, only 1 real answer. done. 2 seconds