Solve e^{2x} -3e^x+2=0, equation for x.

lilyta79jd

lilyta79jd

Answered question

2021-11-17

Solve e2x3ex+2=0, equation for x.

Answer & Explanation

Befoodly

Befoodly

Beginner2021-11-18Added 17 answers

We need to solve following exponential equation:
e2x3ex+2=0
Next we apply substitution ex=t to obtain following quadratic equation:
t23t+2=0
Solution of quadratic equation at2+bt+c=0 is given by formula: t1,2=b±b24ac2a
In our case we have: a=1, b=-3,c=2, so we compute:
t1,2=+3±3241221
=+3±12
t1=3+12=2
t2=312=1
Thus we have two solutions of the quadratic equation:
t1=2 and t2=1
Lets

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