Question

rozwiaż równania ;

oblicz:

a) 4x²-3 =0

b) -1/2x²-8=0

c) x²+2x=0

d) 12x-3x²=0

e) 6x²+1/2x=0

f) Ѵ8x=Ѵ2x²

g) 12x+Ѵ3x²=0

Answer 1

a)

4x²-3 = 0

(2x+√3)(2x-√3) = 0

2x+√3 = 0

2x = -√3  /:2

x = -√3/2

lub

2x-√3 = 0

2x = √3  /:2

x = √3/2

x = -√3/2   v   x = √3/2

 

b)

-1/2x²-8 = 0  I*(-2)

x²+16 = 0

x² ≠ -16, brak pierwiastków rownania.

 

c)

x²+2x = 0

x(x+2) = 0

x = 0 

lub

x+2 = 0

x = -2

x = -2   v   x = 0

 

d)

12x-3x² = 0

3x(4-x) = 0

x = 0

lub

4-x = 0

x = 4

x = 0   v   x = 4

 

e)

6x²+1/2x = 0  I*2

12x²+x = 0

x(12x+1) = 0

x = 0

lub

12x+1 = 0

12x = -1  /:12

x = -1/12

x = -1/12   v   x = 0

 

f)

√8x = √2x²

√2x²-√8x = 0 

√2x²-2√2x = 0 

√2x(x-2) = 0

x = 0

lub

x-2 = 0

x = 2

x = 0    v   x = 2

 

g)

12x+√3x² = 0

√3x²+12x = 0 

x(√3x+12) = 0

x = 0

lub

√3x+12 = 0

√3x = -12  /:√3

x = -12/√3 * √3/√3 = -12√3/3 = -4√3

x = -4√3   v   x = 0