Question

Intervalul caruia ii apartin numerele a, b, c stiind ca a^2+b^2+c^2+38=2(2a+3b+5c) este:

Answer 1

a^2+b^2+c^2+38=4a+6b+10c

a^2-4a+b^2-6b+c^2-10c+4+9+25=0

a^2-2×2×a+4+b^2-2×3×b+9+c^2-2×5×b+25=0

(a-2)^2+(b-3)^2+(c-5)^2=0

Orice nr ridicat la patrat este mai mare sau egal cu 0 =>

(a-2)^2=0 => a-2=0 => a=2

(b-3)^2=0 => b-3=0 => b=3

(c-5)^2=0 => c-5=0 => c=5