Question

Fie expresia
E(x)=(x+5)²+2(x+5)(x-4)+(x-4)², cu x € R
a)Aratati ca E(x)=(2x+1)², oricare ar fi x €R

Answer 1

Explicație pas cu pas:

E(x)=(x+5)²+2(x+5)(x-4)+(x-4)²=>

E(x)=x²+10x+25+2(x²+5x-4x-20)+x²-8x+16 =>

E(x)=x²+10x+25+2(x²+x-20)+x²-8x+16=>

E(x)=2x²+2x+41+2x²+2x-40=>E(x)=4x²+4x+1=> E(x)=(2x+1)²

Answer 2

Răspuns:

    Adevarat!

Explicație pas cu pas:

    (x + 5)² + 2(x + 5)(x - 4) + (x - 4)²

    x² + 2 · 5 · x + 5² + 2(x² - 4x + 5x - 20) + x² - 2 · 4 · x + 4²

    x² + 10x + 25 + 2(x² + x - 20) + x² - 8x + 16

    x² + 10x + 25 + 2x² + 2x - 40 + x² - 8x + 16

    4x² + 4x + 1 = (2x + 1)²