rozwiąż równania
2/x-3 + 4/x+3=
x-5/x + x/x+2=
3x/x+1 - x+2/x -2=
pierwsze zadanie:
2/x-3+4/x+3= 0 dlaczego ?? 2/x-3 = -1/x a 4/x - 3 = 1 -1+1=0
x-5/x + x/x+2=x-5+x/x=2x-5/x
3x/x+1 - x+2/x -2=3x/x+1 - x+3/x -2=2x-3/x+1-2=2x-3/x+1-2x-2/x+1=
=-5/x+1
2/ ( x - 3) + 4/(x + 3) = 0; x różne od 3 i x różne od ( -3)
[ 2*( x + 3)] / ( x^2 - 3^2) + [ 4*( x - 3)]/(x^2 - 3^2) = 0
[ 2 x + 6 + 4 x - 12 ] / (x^2 - 9) = 0
6x - 6 = 0
6 x = 6
x = 1
=============
( x - 5)/ x + x/( x + 2) = 0 ; x różne od 0 i x różne od (-2)
[( x - 5)*(x + 2)]/ [ x*( x + 2)] + [ x*x]/[ x*(x + 2)] = 0
[ x^2 + 2 x - 5 x - 10 ]/( x^2 + 2 x] + x^2 / [ x^2 +2 x] = 0
2 x^2 - 3 x - 10]/( x^2 + 2 x ) = 0
2 x^2 - 3 x - 10 = 0
delta = (-3)^2 - 4*2*(-10) = 9 + 80 = 89
p(delty) = p(89)
x1 = [ 3 - p(89)]/4; x2 = [ 3 + p(89)]/4
=======================================
3x/(x + 1) - ( x + 2)/(x -2) = 0; x różne od ( -1) i x różne od 2
[ 3x*(x -2)]/[ (x +1)*(x - 2)] - [ (x + 1)*(x + 2)]/[ ( x + 1)*( x - 2)] = 0
[ 3 x^2 - 6 x]/[ ( x+1)*( x -2)] - [ x^2 + 2 x + x + 2]/[ (x + 10*(x -2)] = 0
[ 3 x^2 - 6 x - x^2 -3 x - 2 ] / { ( x +1)*(x -2)] = 0
2 x^2 - 9 x - 2 = 0
delta = ( -9)^2 - 4*2*(-2) = 81 + 16 = 97
p(delty) = p(97)
x1 = [ 9 - p(97)]/4 , x2 = [ 9 + p(97)]/4
====================================
p(97) - pierwiastek kwadratowy z 97
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pierwsze zadanie:
2/x-3+4/x+3= 0 dlaczego ?? 2/x-3 = -1/x a 4/x - 3 = 1 -1+1=0
x-5/x + x/x+2=x-5+x/x=2x-5/x
3x/x+1 - x+2/x -2=3x/x+1 - x+3/x -2=2x-3/x+1-2=2x-3/x+1-2x-2/x+1=
=-5/x+1
2/ ( x - 3) + 4/(x + 3) = 0; x różne od 3 i x różne od ( -3)
[ 2*( x + 3)] / ( x^2 - 3^2) + [ 4*( x - 3)]/(x^2 - 3^2) = 0
[ 2 x + 6 + 4 x - 12 ] / (x^2 - 9) = 0
6x - 6 = 0
6 x = 6
x = 1
=============
( x - 5)/ x + x/( x + 2) = 0 ; x różne od 0 i x różne od (-2)
[( x - 5)*(x + 2)]/ [ x*( x + 2)] + [ x*x]/[ x*(x + 2)] = 0
[ x^2 + 2 x - 5 x - 10 ]/( x^2 + 2 x] + x^2 / [ x^2 +2 x] = 0
2 x^2 - 3 x - 10]/( x^2 + 2 x ) = 0
2 x^2 - 3 x - 10 = 0
delta = (-3)^2 - 4*2*(-10) = 9 + 80 = 89
p(delty) = p(89)
x1 = [ 3 - p(89)]/4; x2 = [ 3 + p(89)]/4
=======================================
3x/(x + 1) - ( x + 2)/(x -2) = 0; x różne od ( -1) i x różne od 2
[ 3x*(x -2)]/[ (x +1)*(x - 2)] - [ (x + 1)*(x + 2)]/[ ( x + 1)*( x - 2)] = 0
[ 3 x^2 - 6 x]/[ ( x+1)*( x -2)] - [ x^2 + 2 x + x + 2]/[ (x + 10*(x -2)] = 0
[ 3 x^2 - 6 x - x^2 -3 x - 2 ] / { ( x +1)*(x -2)] = 0
2 x^2 - 9 x - 2 = 0
delta = ( -9)^2 - 4*2*(-2) = 81 + 16 = 97
p(delty) = p(97)
x1 = [ 9 - p(97)]/4 , x2 = [ 9 + p(97)]/4
====================================
p(97) - pierwiastek kwadratowy z 97