Please solve for this
e^(x) - e^(-x)=2
Hello, camherokid!
Solve for x: .e^x - e^{-x} .= .2
Multiply by e^x: .e^{2x} - 1 .= .2·e^x
And we have: . (e^x)² - 2·e^x - 1 .= .0 . . . a quadratic equation
. . . . . . . . . . . . . . . . . . . . . . . . __________
. . . . . . . . . . . . . . . . . . . . 2 ± √2² - 4(1)(-1)
Quaratic Formula: . e^x .= . ----------------------- . = . 1 ± √2
. . . . . . . . . . . . . . . . . . . . . . . . 2(1)
Since e^x is positive: . e^x .= .1 + √2
. . Therefore: . x .= .ln(1 + √2)