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D( x )
x^2-11 = 0
x^2-11 = 0
x^2-11 = 0
1*x^2 = 11 // : 1
x^2 = 11
x^2 = 11 // ^ 1/2
abs(x) = 11^(1/2)
x = 11^(1/2) or x = -11^(1/2)
x in (-oo:-11^(1/2)) U (-11^(1/2):11^(1/2)) U (11^(1/2):+oo)
-18/(x^2-11) = x^2 // - x^2
-18/(x^2-11)-x^2 = 0
(-x^2*(x^2-11))/(x^2-11)-18/(x^2-11) = 0
-x^2*(x^2-11)-18 = 0
11*x^2-x^4-18 = 0
11*x^2-x^4-18 = 0
11*x^2-x^4-18 = 0
{ 1, -1, 2, -2, 3, -3, 6, -6, 9, -9, 18, -18 }
1
x = 1
11*x^2-x^4-18 = -8
1
-1
x = -1
11*x^2-x^4-18 = -8
-1
2
x = 2
11*x^2-x^4-18 = 10
2
-2
x = -2
11*x^2-x^4-18 = 10
-2
3
x = 3
11*x^2-x^4-18 = 0
3
x-3
2*x-x^3-3*x^2+6
11*x^2-x^4-18
x-3
x^4-3*x^3
11*x^2-3*x^3-18
3*x^3-9*x^2
2*x^2-18
6*x-2*x^2
6*x-18
18-6*x
0
2*x-x^3-3*x^2+6 = 0
{ 1, -1, 2, -2, 3, -3, 6, -6 }
1
x = 1
2*x-x^3-3*x^2+6 = 4
1
-1
x = -1
2*x-x^3-3*x^2+6 = 2
-1
2
x = 2
2*x-x^3-3*x^2+6 = -10
2
-2
x = -2
2*x-x^3-3*x^2+6 = -2
-2
3
x = 3
2*x-x^3-3*x^2+6 = -42
3
-3
x = -3
2*x-x^3-3*x^2+6 = 0
-3
x+3
2-x^2
2*x-x^3-3*x^2+6
x+3
x^3+3*x^2
2*x+6
-2*x-6
0
2-x^2 = 0
DELTA = 0^2-(-1*2*4)
DELTA = 8
DELTA > 0
x = (8^(1/2)+0)/(-1*2) or x = (0-8^(1/2))/(-1*2)
x = -2^(1/2) or x = 2^(1/2)
x in { -2^(1/2), 2^(1/2), 3, -3}
(x+2^(1/2))*(x-2^(1/2))*(x-3)*(x+3) = 0
((x+2^(1/2))*(x-2^(1/2))*(x-3)*(x+3))/(x^2-11) = 0
((x+2^(1/2))*(x-2^(1/2))*(x-3)*(x+3))/(x^2-11) = 0 // * x^2-11
(x+2^(1/2))*(x-2^(1/2))*(x-3)*(x+3) = 0
( x+2^(1/2) )
x+2^(1/2) = 0 // - 2^(1/2)
x = -2^(1/2)
( x+3 )
x+3 = 0 // - 3
x = -3
( x-2^(1/2) )
x-2^(1/2) = 0 // + 2^(1/2)
x = 2^(1/2)
( x-3 )
x-3 = 0 // + 3
x = 3
x in { -2^(1/2), -3, 2^(1/2), 3 }
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