Question

Please help! Solve this​

Answer 1

The solution to $\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2$ is x = 1

How to solve the equation?

The equation is given as:

$\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2$

Split the equation as follows:

$y\ =\ \left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}$

$y = 1 + x^2$

Next, we plot the graph of both equations (see attachment)

From the attached graph, the intersection point is (1, 2)

Remove the y value

x = 1

Hence, the solution to $\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2$ is x = 1

Read more about equations at:

brainly.com/question/2972832

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