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produsul a doua numere este 420. Marind unul dintre termeni cu 5 si micsorand celalalt termen cu 2 , produsul numerelor devine 400 . Determinati numerele.
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Răspuns :

a*b=420⇒a=420/b
(a+5)(b-2)=400
ab+5b-2a-10=400
420+5b-2*420/b=410
5b-840/b=-10
5b-840/b+10=0
5b²+10b-840=0
[tex]\Delta=100+16800=16900=\ \textgreater \ \sqrt{\Delta}=130\\ b_{1,2}=\frac{-10+-130}{10}\\ b_1=\frac{120}{10}=12\\ b_2=\frac{-140}{10}=-14\\ a)b=12=\ \textgreater \ a*12=420=\ \textgreater \ a=35\\ b)b=-14=\ \textgreater \ a*(-14)=420=\ \textgreater \ a=-30\\ (a,b) apartine \{ (35,12),(-30,-14)\} [/tex]