Question

determinati solutiile ecuatiilor:
a)rad5(x+4)+2rad5(x-2)=rad15
b)x(2rad2-rad3)+2x(rad3-rad2)=6+rad3
c)xrad2+2x(rad8-3)=20-6x
d)2x(2+rad3)-(rad3-1)(x+2)=2x+6

Answer 1

a)√5(x+4)+2√5(x-2)=x√5+4√5+2x√5-4√5=x√5+2x√5=3x√5
b)x(2√2-√3)+2x(√3-√2)=6+√3
2x√2-x√3+2x√3-2x√2=6+√3
-x√3+2x√3=6+√3
x√3=6+√3
x=6+√3/√3  rationalizam
x=√3(6+√3)/3=6√3+3/3
x=3(2√3+1)/3  se simplifica
x=2√3+1
c)x√2+2x(√8-3)=20-6x
x√2+2x(2√2-3)=20-6x
x√2+4x√2-6x=20-6x
5x√2=20-6x+6x
5x√2=20
x√2=4
x=4/√2 rationalizam
x=4√2/2=2√2
d)2x(2+√3)-(√3-1)(x+2)=2x+6
4x+2x√3-(x√3+2√3-x-2)=2x+6
4x+2x√3-x√3-2√3+x+2=2x+6
x√3-2√3+5x+2=2x+6
x√3-2√3=2x+6-5x-2
x√3-2√3=-3x+4
x√3+3x=4+2√3
x(√3+3)=2(2+√3)