Odpowiedź:
a⁴ + b⁴ = 3,5
Wyjaśnienie:
[tex]a+b = 1\\a^{2}+b^{2} = 2\\a^{4} + b^{4} = ?\\\\a^{4}+b^{4} = (a^{2}+b^{2})^{2} - 2(ab)^{2}\\\\a^{2}+b^{2} = (a+b)^{2}-2ab\\\\2 = 1^{2}-2ab\\\\2ab = 1-2\\\\2ab = -1 \ \ /:2\\\\ab = -\frac{1}{2}\\\\a^{4}+b^{4} = 2^{2}-2(-\frac{1}{2})^{2} = 4-2\cdot\frac{1}{4} = 4-\frac{1}{2} = 3,5[/tex]
