Question

Află valorile lui a, b, c dacă verifică simultan relațiile:b+c=7; a+b=5; a×b+b×c=18.

Answer 1

b+c=7
a+b=5
........
a+2b+c=12
a+c=12-2b
a*b+b*c=18
b(a+c)=18
b*(12-2b)=18
-2b²+12b=18
-2b²+12b-18=0
2b²-12b+18=0
b²-6b+9=0
(b-3)²=0
b-3=0⇒b=3
a+3=5⇒a=2
3+c=7⇒c=4

Answer 2

[tex]b+c = 7 \implies c = 7-b a +b = 5 \implies a = 5 - b (5-b)*b+b*(7-b)=18 \implies 5b-b^2+7b-b^2=18 b^2-6b+9=0\implies(b-3)^2=0 \implies b-3 = 0\implies b = 3 c = 7-3 = 4 a = 5-3 = 2[/tex]