Odpowiedź:
[tex]a-b=10\\ab=6\\\\a=10 +b\\(10+b)b=6\\\\b^{2}+10b-6=0\\[/tex]
Δ[tex]= 100-4*(-6) = 124[/tex]
[tex]b_{1}=\frac{-10+\sqrt{124} }{2}\\b_{2}=\frac{-10-\sqrt{124} }{2}\\ \\\\a_{1}=10 + \frac{-10+\sqrt{124} }{2}= \frac{20}{2} + \frac{-10+\sqrt{124} }{2} = \frac{10+\sqrt{124} }{2}\\a_{2}=10+\frac{-10-\sqrt{124} }{2} =\frac{20}{10} + \frac{-10-\sqrt{124} }{2}=\frac{10-\sqrt{124} }{2} \\[/tex]
[tex]a_{1} ^{2} +b_{1} ^{2} = (\frac{10+\sqrt{124} }{2} )^{2} + (\frac{-10+\sqrt{124} }{2} )^{2} =\\\frac{(10+\sqrt{124} )^{2} }{4}+\frac{(-10+\sqrt{124} )^{2} }{4} = \frac{100+20\sqrt{124}+124}{4} + \frac{100-20\sqrt{124}+124}{4} =\frac{448}{4}=112\\ \\[/tex]
[tex]a_{2} ^{2} +b_{2} ^{2} = (\frac{10-\sqrt{124} }{2} )^{2} + (\frac{-10-\sqrt{124} }{2} )^{2} =\\\frac{(10-\sqrt{124} )^{2} }{4}+\frac{(-10-\sqrt{124} )^{2} }{4} = \frac{100-20\sqrt{124}+124}{4} + \frac{100+20\sqrt{124}+124}{4} =\frac{448}{4}=112\\ \\[/tex]
Odpowiedz D)
