Question

27 Rezolvați ecuațiile:
a 2x(4+2√3)-√3(5x+3√3)=2√3(3√3-x)+2(4x-9);
b (√5-2√3).x+2x(√5 +√3)=√125+2x√5;
c 2-√3+2x(2-√3)= 4(x-√3)+√27;
x√2+1+√√2+x(1+√2) + x(3+2√2)=5(3+√2)-2(3+2√2);
e √5-2+x(√5-2) = x(2+√5)-(√5+2);
+ √3(√2x+1)+√2(√3x+1)=2x(√6 +1)-(√3-√2).





ex de jos va rog dau coroana

Answer 1

Răspuns:

Explicație pas cu pas:

27 Rezolvați ecuațiile:

a. 2x(4+2√3)-√3(5x+3√3)=2√3(3√3-x)+2(4x-9)  ⇔

8x+4x√3-5x√3-9=18-2x√3+8x-18  ⇔-x√3+2x√3=9  ⇔x√3=9  ⇔

x=9/√3=9√3/3=3√3

b. (√5-2√3).x+2x(√5 +√3)=√125+2x√5  ⇔

x√5-2x√3+2x√5+2x√3=5√5+2x√5  ⇔x√5=5√5  ⇔x=5√5/√5=5  

c. 2-√3+2x(2-√3)= 4(x-√3)+√27 ⇔2-√3+4x-2x√3=4x-4√3+3√3  ⇔

2-√3+√3=2x√3  ⇔ 2=2x√3  ⇔x=2/2√3=√3/3

d. x√2+1+√2+x(1+√2) + x(3+2√2)=5(3+√2)-2(3+2√2) ⇔

x√2+1+√2+x+x√2+3x+2x√2=15+5√2-6-4√2  ⇔  4x√2+4x=9+√2-1-√2  ⇔

4x(√2+1)=8  ⇔x=8/4(√2+1)  ⇔x=2/(√2+1)=2(√2-1)/(2-1)=2(√2-1)

e. √5-2+x(√5-2) = x(2+√5)-(√5+2) ⇔√5-2+x√5-2x=2x+x√5-√5-2  ⇔

√5-2+√5+2=4x  ⇔2√5=4x  ⇔ x=2√5/4=√5/2

f. √3(√2x+1)+√2(√3x+1)=2x(√6 +1)-(√3-√2) ⇔ x√6+√3+x√6+√2=2x√6+2x-√3+√2  ⇔√3+√2=2x-√3+√2 ⇔2√3=2x  ⇔ x=2√3/2 =√3