←Vrati se na zadatke2. ZadatakAko su a≠0a\ne0a=0 i b≠0b\ne0b=0 dva međusobno različita realna broja za koje vrijedi a2017+2017a=b2017+2017b,\frac{a}{2017}+\frac{2017}{a}=\frac{b}{2017}+\frac{2017}{b},2017a+a2017=2017b+b2017, izračunajte a⋅b\sqrt{a\cdot b}a⋅b.Prikaži rješenjeRješenjeZapišimo danu jednakost u sljedećem obliku: a2017+2017a=b2017+2017b\frac{a}{2017}+\frac{2017}{a}=\frac{b}{2017}+\frac{2017}{b}2017a+a2017=2017b+b2017 ⟺12017(a−b)=2017(1b−1a)\Longleftrightarrow \frac{1}{2017}(a-b)=2017\left(\frac1b-\frac1a\right)⟺20171(a−b)=2017(b1−a1) ⟺12017(a−b)=2017(a−bab)\Longleftrightarrow \frac{1}{2017}(a-b)=2017\left(\frac{a-b}{ab}\right)⟺20171(a−b)=2017(aba−b) ⟺(a−b)(12017−2017ab)=0.\Longleftrightarrow (a-b)\left(\frac{1}{2017}-\frac{2017}{ab}\right)=0.⟺(a−b)(20171−ab2017)=0. Kako je a≠0a\ne0a=0, b≠0b\ne0b=0 i a≠ba\ne ba=b, slijedi 12017−2017ab=0.\frac{1}{2017}-\frac{2017}{ab}=0.20171−ab2017=0. Tada je 12017=2017ab\frac1{2017}=\frac{2017}{ab}20171=ab2017, odnosno ab=2017.\sqrt{ab}=2017.ab=2017.Pomakni formulu lijevo ili desno.
