[tex](a+b)^2=a^2+2ab+b^2\\\\1^2=2+2ab\\\\1-2=2ab\\\\2ab=-1\ \ \ |:2\\\\ab=-\frac{1}{2}\ \ \ |()^2\\\\a^2b^2=\frac{1}{4}\\\\\\\\(a^2+b^2)^2=a^4+2a^2b^2+b^4\\\\a^4+b^4=(a^2+b^2)^2-2a^2b^2\\\\a^4+b^4=2^2-2\cdot\frac{1}{4}\\\\a^4+b^4=4-\frac{1}{2}\\\\a^4+b^4=3\frac{1}{2}\\[/tex]
