Question

Rozwiąż równania.

a) 3x-x√5=2+√5

b)x-1=√13(x-3)

c)2x-√2=x√2-1

d)x+2=√2(x+1)

Answer 1

a)

3x-x√5=2+√5

x(3-√5)=2+√5

x=(2+√5)/(3-√5)

x=(2+√5)(3+√5)/(3-√5)(3+√5)

x=(6+2√5+3√5+5)/(9-5)

x=¼(11+5√5)

 

b)
x-1=√13(x-3)

x-1=x√13-3√13

x-x√13=-3√13+1

x(1-√13)=-3√13+1

x=(-3√13+1)/(1-√13)

x=(-3√13+1)(1+√13)/(1-√13)(1+√13)

x=(-3√13-39+1+√13)/(1-13)

x=(-38-2√13)/(-12)

x=1/12(38+2√13)

 

c)

2x-√2=x√2-1

2x-x√2=-1+√2

x(2-√2)=-1+√2

x=(-1+√2)/(2-√2)

x=(-1+√2)(2+√2)/(2-√2)(2+√2)

x=(-2-√2+2√2+2)/(4-2)

x=√2/2

 

d)

x+2=√2(x+1)

x+2=x√2+√2

x-x√2=√2-2

x(1-√2)=√2-2

x=(√2-2)/(1-√2)

x=(√2-2)(1+√2)/(1-√2)(1+√2)

x=(√2+2-2-2√2)/(1-2)

x=(-√2)/(-1)

x=√2