Question
Question: How do you solve \[{{e}^{2x}}-6{{e}^{x}}-16=0\]?...
How do you solve e2x−6ex−16=0?
Solution
To solve the given question, we should know how to find the roots of a quadratic equation. For a general quadratic equation ax2+bx+c=0, using the quadratic formula method we can find the roots of the equation as x=2a−b±b2−4ac. We can find the roots by substituting the coefficients in this formula.
Complete step-by-step solution:
We are given the equation e2x−6ex−16=0, we have to solve this equation. The given equation can also be expressed as,
(ex)2−6ex−16=0
Substituting ex=t in the above equation, it can be expressed as
⇒t2−6t−16=0
We get a quadratic equation in t. We know that for a general quadratic equation ax2+bx+c=0, using the formula method we can find the roots of the equation as x=2a−b±b2−4ac.
Substituting the value of coefficients, we get