Simplifying
4x3 + -81x = 0
Reorder the terms:
-81x + 4x3 = 0
Solving
-81x + 4x3 = 0
Solving for variable 'x'.
Factor out the Greatest Common Factor (GCF), 'x'.
x(-81 + 4x2) = 0
Factor a difference between two squares.
x((9 + 2x)(-9 + 2x)) = 0
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:
Simplifying
x = 0
Solving
x = 0
Move all terms containing x to the left, all other terms to the right.
Simplifying
x = 0
Subproblem 2
Set the factor '(9 + 2x)' equal to zero and attempt to solve:
Simplifying
9 + 2x = 0
Solving
9 + 2x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-9' to each side of the equation.
9 + -9 + 2x = 0 + -9
Combine like terms: 9 + -9 = 0
0 + 2x = 0 + -9
2x = 0 + -9
Combine like terms: 0 + -9 = -9
2x = -9
Divide each side by '2'.
x = -4.5
Simplifying
x = -4.5
Subproblem 3
Set the factor '(-9 + 2x)' equal to zero and attempt to solve:
Simplifying
-9 + 2x = 0
Solving
-9 + 2x = 0
Move all terms containing x to the left, all other terms to the right.
Add '9' to each side of the equation.
-9 + 9 + 2x = 0 + 9
Combine like terms: -9 + 9 = 0
0 + 2x = 0 + 9
2x = 0 + 9
Combine like terms: 0 + 9 = 9
2x = 9
Divide each side by '2'.
x = 4.5
Simplifying
x = 4.5
Solution
x = {0, -4.5, 4.5}
3/(х²-4х+4) - 4(х²-4) = 1/(х+2),
3/(х-2)² - 4(х-2)(х+2) = 1/(х+2),
(общий знаменатель будет равен (х+2)(х-2)²)
3(х+2)/(х+2)(х-2)² - 4(х-2)/(х+2)(х-2²) = 1(х-2)²/(х+2)(х-2)²,
(3х+6)/(х-2)² - (4х-8)/(х+2)(х-2)² = (х²-4х+4)/(х+2)(х-2)²,
(3х+6 - 4х+8 - х²+4х-4) / (х+2)(х-2)² = 0,
(- х²+3х+10) / (х+2)(х-2)² = 0,
ОДЗ:
х+2 ≠ 0, (х-2)² ≠ 0,
х ≠ -2, х-2 ≠ 0,
х ≠ 2,
- х²+3х+10 = 0,
х² - 3х - 10 = 0,
Д = (-3)² - 4*1*(-10) = 9 + 40 = 49,
х1 = (3 + 7)/2 = 10/2 = 5,
х2 = (3 - 7)/2 = -4/2 = -2 - не подходит,
ответ: х = 5
