Question

1.determinati valoarea minima a expresiei :
a la a doua + b la a doua - 6a +10b+40
2. Determinati valoarea maxima a expresiei :
-x la a doua +8x-30

dau coroana

Answer 1

1.E=a^2+b^2-6a+10b+40=a^2-6a+9+b^2+10b+25+6=(a-3)^2+(b+5)^2+6
(a-3)^2>=0
(b+5)^2>=0
deci E>=6 valoarea minimă=6
2.E=-x^2+8x-30=-(x^2-8x+30)=-(x^2-8x+16+14)=-(x-4)^2-14
(x-4)^2 >=0
-(x-4)^2 <=0
deci E <=-14 valoarea maximă=-14