Question

Fie expresia E(x)=(x+3)^2-(x+2)^2, unde x€R. Calculați E(√3-1)​

Answer 1

Răspuns:

Explicație pas cu pas:

Fie expresia E(x)=(x+3)^2-(x+2)^2, unde x€R. Calculați E(√3-1)​.

E(x)=(x+3)²-(x+2)²=(x+3+x+2)(x+3-x-2)=(2x+5)·1=2x+5

Am folosit formula de calcul prescurtat a²-b²=(a+b)(a-b)

E(x)=2x+5

E(√3-1)=2(√3-1)+5=2√3-2+5=2√3+3

E(√3-1)=2√3+3

Answer 2

E(√3-1) = [(√3-1) + 3]^2 - [(√3-1) + 2]^2
= (√3+2)^2 - (√3)^2
= (√3+2 + √3)(√3+2 - √3)
= (2√3 + 2)(2√3)
= (2√3 + 2)(2√3)
= 4√3^2 + 4√3
= 4(3)^(1/2) + 4√3

Astfel, E(√3-1) = 4√3 + 4√3 = 8√3.