Question

determina nr nat a caror suma si produs este 22

Answer 1

a+b = 22  => a = 22-b
a×b = 22  => (22-b)×b=22
=>$-b^{2} +22b = 22 \\ -b^{2} +22b -22=0 \\b^{2} -22b + 22=0$
Δ=484-88=396
$b_{1,2} = \frac{22+- \sqrt{396} }{2} = \frac{22+- 6\sqrt{11} }{2} =11+-3 \sqrt{11}$

$b_{1} =11+3 \sqrt{11}\\a_{1}+11+3 \sqrt{11}=22 \\a_{1}= 22-11-3 \sqrt{11} \\a_{1}= 11-3 \sqrt{11}$

$b_{2} =11-3 \sqrt{11} \a_{2}+11-3 \sqrt{11}=22 \\a_{2}= 22-11+3 \sqrt{11} \\a_{2}= 11+3 \sqrt{11}$

=>  Solutia (1) 
      a=11-3√11
      b=11+3√11

=>  Solutia (2)
      a = 11+3√11
      b = 11-3√11