a+b = 22 => a = 22-b
a×b = 22 => (22-b)×b=22
=>[tex]-b^{2} +22b = 22 \\ -b^{2} +22b -22=0 \\b^{2} -22b + 22=0[/tex]
Δ=484-88=396
[tex] b_{1,2} = \frac{22+- \sqrt{396} }{2} = \frac{22+- 6\sqrt{11} }{2} =11+-3 \sqrt{11} [/tex]
[tex] b_{1} =11+3 \sqrt{11}\\a_{1}+11+3 \sqrt{11}=22 \\a_{1}= 22-11-3 \sqrt{11} \\a_{1}= 11-3 \sqrt{11} [/tex]
[tex] b_{2} =11-3 \sqrt{11} \a_{2}+11-3 \sqrt{11}=22 \\a_{2}= 22-11+3 \sqrt{11} \\a_{2}= 11+3 \sqrt{11} [/tex]
=> Solutia (1)
a=11-3√11
b=11+3√11
=> Solutia (2)
a = 11+3√11
b = 11-3√11
