Question

determinati solutiile ecuatiilor:
a)x√2+x√8+x√32=√4+√16+√46
b)√5(x+4)+2√5(x-2)=√15
c)x(2√2-√3)+2x(√3-√2)=6+√3
d)x√2+2x(√8-3)=20-6x

Answer 1

a) √2x+2√2x+4√2x=2+4+√46
7√2x=6+√46
x=(6+√46)/7√2
x=(6√2+2√46)/14

b) √5x+4√5+2√5x-4√5=√15
3√5x=√15
x=√15/3√5
x=√3/3

c) 2√2x-√3x+2√3x-2√2x=6+√3
√3x=6+√3
x=(6+√3)/√3
x=(6√3+3)/3
x=2√3+1

d) √2x +4√2x-6x=20-6x
5√2x=20
√2x=4
x=2√2

Answer 2

a)x√2+x√8+x√32=√4+√16+√46

x√2+2x√2+4x√2=2+4+√46

7x√2=6+√46

x=(6+√46)/7√2

x=[(6+√46)√2]/14

b)√5(x+4)+2√5(x-2)=√15

x√5+4√5+2x√5-4=√15

3x√5=√15-4√5

x=[(√15-4√5)·√5]/15

c)x(2√2-√3)+2x(√3-√2)=6+√3

2x√2-x√3+2x√3-2x√2=6+√3

x√3=6+√3

x=(6+√3)/√3

x=(6√3+3)/3

x=3(2√3+1)/3

x=2√3+1


d)x√2+2x(√8-3)=20-6x

x√2+2x√8-6x=20-6x

x√2+4x√2=20

5x√2=20

x=20/5√2

x=(20√2)/10

x=2√2