Question

Repede !! Dau coroană !!

Să se arate că expresia E=2(3x+1)(1-3x)+(3x-2)²+(3x+2)² nu depinde de x .

Answer 1

Răspuns:

Explicație pas cu pas:

poza

Answer 2

E(x)=2(1+3x)(1-3x)+(3x-2)^2+(3x+2)^2

(A+B)(A-B)=A^2-B^2<=>(1+3x)(1-3x)=1^2-(3x)^2=1-9x^2

(A-B)^2=A^2-2AB+B^2<=>(3x-2)^2=(3x)^2-2*3x*2+(-2)^2=9x^2-12x+4

(A+B)^2=A^2+2AB+B^2<=>(3x+2)^2=(3x)^2+2*3x*2+2^2=9x^2+12x+4

E(x)=2(1-9x^2)+9x^2-12x+4+9x^2+12x+4

E(x)=2*1+2*(-9x)^2+18x^2+8

E(x)=2-18x^2+18x^2+8

E(x)=2+8

E(x)=10