Quadratic Exponential Equation?!

Algebra Level 3

Find the sum of all real values of x such that:

2 x = x 2 2^x = x^2

Round your answer to 2 decimal places


The answer is 5.23.

Hans Gabriel Daduya by Hans Gabriel Daduya , 20, Philippines

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1 solution

Vilakshan Gupta
Dec 6, 2017

The intersection points of graphs of functions y = 2 x y=2^x and y = x 2 y=x^2 are the required solutions of x x .

The solutions are x = 2 x=2 , x = 4 x=4 and x ≈ − 0.76 x \approx -0.76 . Therefore sum of all solutions ≈ 5.23 \approx \boxed{ 5.23}

2 Helpful 1 Interesting 0 Brilliant 0 Confused

Can you solve this without using a Wolphram Alpha?

Hans Gabriel Daduya - 3 years, 6 months ago

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I have just taken the graph from Wolphram Alpha. I could have taken the graph from somewhere else also, Basically what i mean is, where both these graphs will intersect will give us a solution. i don't know an algebraic solution to this problem. If you know, then please share it with me. Thanks.

Vilakshan Gupta - 3 years, 6 months ago

how do we find x=-.76

Manju Prasath - 3 years ago

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We cannot find it manually (From elementary mathematics) , so we have to find it from graph only, that's the only way out.

Vilakshan Gupta - 3 years ago

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