Réponse :
Bonsoir,
Explications étape par étape
[tex]a+b=1\\\\a^2+b^2=2\\\\(a+b)^2=a^2+b^2+2ab\\1^2=2+2ab\\2ab=-1\\\\\boxed{ab=\dfrac{-1}{2}}\\ \\(a^2+b^2)^2=a^4+b^4+2a^2b^2\\2^2=a^4+b^4+2*(\dfrac{-1}{2})^2\\\\a^4+b^4=4-2*\dfrac{1}{4}=4-\dfrac{1}{2}\\\\\boxed{a^4+b^4=\dfrac{7}{2}}\\\\\\(a^4+b^4)*(a^2+b^2)=a^6+b^6+a^2b^4+a^4b^2=a^6+b^6+a^2b^2(a^2+b^2)\\\\a^6+b^6=(a^4+b^4)*(a^2+b^2)-a^2b^2(a^2+b^2)\\ \\a^6+b^6=\dfrac{7}{2} *2-(\dfrac{-1}{2})^2*2\\a^6+b^6=7-\dfrac{1}{2}\\\\\\\boxed{a^6+b^6=\dfrac{13}{2}}[/tex]
