Question

Solve equation e^{2x} + 2e^{x} −3 = 0

Answer 1

$e^{2x}+2e^x-3=0\\\\\underbrace{\left(e^x\right)^2+2e^x\cdot1+1^2}_{(*)}-1^2-3=0\\\\(e^x+1)^2-1-3=0\\\\(e^x+1)^2-4=0\\\\(e^x+1)^2=4\iff e^x+1=\sqrt4\to e^x+1=2\\\\e^x=2-1\\\\e^x=1\\\\e^x=e^0\iff x=0$