Question

1]. -8xdo pot.2+10x do pot.3-2xdo pot.4=0 rozwiaz rownanie 2.]wyznacz dziedzine wyrazenia i zapisz je w najprostszej postaci x+1 kreska ulam.xdo pot.2-2x-x+2kres.ul.xdo 2-4

Answer 1

1.

-8x²+10x³-2x⁴ = 0   /:(-2)

4x²-5x³+x⁴ = 0

x²(4-5x+x²) = 0

x² = 0   => x = 0

lub

x²-5x+4 = 0

Δ = b²-4ac = 25-16 = 9

√Δ = √9 = 3 

x1 = (-b-√Δ)/2a = (5-3)/2 = 1

x2 = (-b+√Δ)/2a = (5+3)/2 = 4

Odp. x = 0   v   x = 1   v   x = 4

 

2.

 x+1            x+2

--------   -   --------

x²-2x          x²-4

 

Z: x²-2x ≠ 0

    x(x-2) ≠ 0

    x ≠ 0

    x ≠ 2

 

    x²-4 ≠ 0

    (x+2)(x-2) ≠ 0

     x ≠ -2

     x ≠ 2

D = R \ {-2; 0; 2}

 

 x+1            x+2            x+1              x+2                 x+1               1             x+1-x

--------   -   -------   =   ---------   -   --------------   =   ----------   -   --------   =   ---------   =

x²-2x          x²-4          x(x-2)         (x+2)(x-2)          x(x-2)           x-2            x(x-2)

 

          1  

=    ----------

        x²-2x