Question

E^(2x)-e^(x)-2=0 Round to the nearest hundredth if necessary.

Answer 1

Let's denote e^x as u.

The equation can be written as u^2 - u - 2 = 0.

Factoring the quadratic equation, we have (u - 2)(u + 1) = 0.

Setting each factor equal to zero, we obtain u - 2 = 0 and u + 1 = 0.

Solving the equations, we find u = 2 and u = -1.

Since e^x cannot be negative, we discard u = -1.

Hence, e^x = 2.

Taking the natural logarithm of both sides, we have x = ln(2).

Round to the nearest hundredth, x = 0.69. Answer: \boxed{0.69}.

Explanation: