Bonjour
Nola365
[tex]a^2+b^2=2\Longrightarrow(a^2+b^2)^2=2^2\\\\\Longrightarrow a^4+2a^2b^2+b^4=4\\\\\Longrightarrow\boxed{a^4+b^4=4-2a^2b^2}\\\\or\ a+b=1\Longrightarrow(a+b)^2=1^2\Longrightarrow a^2+2ab+b^2=1\\\\\Longrightarrow(a^2+b^2)+2ab=1\\\\\Longrightarrow2+2ab=1\\\\\Longrightarrow2ab=-1\\\\\Longrightarrow(2ab)^2=(-1)^2\\\\\Longrightarrow4a^2b^2=1\\\\\Longrightarrow\boxed{2a^2b^2=\dfrac{1}{2}}[/tex]
D'où
[tex]a^4+b^4=4-\dfrac{1}{2}\\\\a^4+b^4=\dfrac{8}{2}-\dfrac{1}{2}\\\\\\\Longrightarrow\boxed{a^4+b^4=\dfrac{7}{2}=3,5}[/tex]
