Question

Ajutorrr va rogggg helpppp​

Answer 1

Explicație pas cu pas:

E=x²+y²-4x+6y+25=>

E=x²-4x+4+y²+6y+9+12 =>

E=(x+2)²+(y+3)²+12 =>min E=12 (pt ca (x+2)² si (y+3)² sunt >=0 deci minimul expresiei se va face pt minimul lor adica 0)

F=2x²+5y²-4xy+8x+4y+25 =>

F=x²+8x+16+y²+4y+4+x²-4xy+4y²+5 =>

F=(x+4)²+(y+2)²+(x-2y)²+5 => min F=5

G=V(4x²+4x+5)+V(9y²-12y+13)+V(16z²+24z+25) =>

G=V(4x²+4x+1+4)+V(9y²-12y+4+9)+V(16z²+24z+9+16)=>

G=V[(2x+1)²+4] + V[(3y-2)²+9] + V[(4z+3)²+16]

Cum avem (2x+1)², (3y-2)² si (4z+3)² stim ca ele sunt >=0 deci min G=V(0+4)+V(0+9)+V(0+16)=>minG=9

x²+y²>=(x+y)²/2 => 2x²+2y²>=(x+y)²=>2x²+2y²>=x²+2xy+y² =>x²+y²>=2xy => x²+y²-2xy>=0 => (x-y)²>= 0 (A)