Question 188046
{{{e^x+e^(-x)=7}}} Start with the given equation



{{{e^x+1/e^x=7}}} Rewrite {{{e^(-x)}}} as {{{1/e^x}}}



Now let {{{u=e^x}}}



{{{u+1/u=7}}} Replace each term {{{e^x}}} with "u"



{{{u^2+1=7u}}} Multiply EVERY term by the LCD "u" to clear the fractions.



{{{u^2-7u+1=0}}} Subtract 7u from both sides.



Now use the quadratic equation to solve for "u". Once you have the solutions in terms of "u", substitute {{{u=e^x}}} back in to solve for "x".