Question

Solve the equation algebraically. Calculus section 1.5 of textbook 2^x + 2^-x = 5

Answer 1

The value of x from the given expression is $\frac{5+\sqrt{29}}{2log2}$

Solving quadratic expression

Given the algebraic expression below;

2^x + 2^-x = 5

This can also be expressed as:

1/2^x+ 1/2^x = 5

Let P = 2^x, such that;

P + 1/P = 5

P²-1/P = 5

P²-1 = 5P

P²-5P-1=0

On factrorizing, then;

P = $\frac{5+\sqrt{29}}{2}$

Since 2^x = P, then;

$2^x=\frac{5+\sqrt{29}}{2} \\\\xlog2=\frac{5+\sqrt{29}}{2} \\\\x=\frac{5+\sqrt{29}}{2log2}$

Hence the value of x from the given expression is $\frac{5+\sqrt{29}}{2log2}$

Learn more on algebraic equation here: brainly.com/question/723406

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