Question

E(x)=2(x+3)^2-(2+x)(x-2)-2(5x+7), unde x este nr real.
Demonstrati ca E(x)>sau egal cu 7, pt orice nr real.​

Answer 1

2(x+3)^2-(2+x)(x-2)-2(5x+7) >= 7

<=> 2(x^2+6x+9)-(x^2-4)-10x-14-7 >= 0

<=> 2x^2+12x+18-x^2+4-10x-21 >= 0

<=> x^2+2x+1 >= 0

<=> (x+1)^2 >= 0 (A)