Question

Se da expresia E(x)= ( x² - x+ 2)² – ( x²- x)²- 4(x²-x+1), unde x € R
Aratati ca E(x) nu depinde de x


*€ =apartine*
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Answer 1

Explicație pas cu pas:

E(x)=(x²-x+2)²-(x²-x)²-4(x²-x+1)=>

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

E(x)=2(2x²-2x+2)-4(x²-x+1)=>

E(x)=4(x²-x+1)-4(x²-x+1)=>E(x)=0 val. constanta