Мой запрос в chat gpt "x^3-7x+6=0 provide a solution".
Её ответ:
To solve the equation x^3 - 7x + 6 = 0, we can start by factoring the left-hand side of the equation.
One way to factor this equation is to factor out a greatest common factor (GCF) from the left-hand side. In this case, the GCF is 1, so we can write:
x^3 - 7x + 6 = (x-1)(x^2 + x - 6) = 0
Now we have a quadratic equation in the form of (x-1) (x^2 + x - 6) = 0. Using the zero product property, we know that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, either x-1 = 0 or x^2 + x - 6 = 0.
Solving for x-1 = 0, we find that x = 1.
To solve the quadratic equation x^2 + x - 6 = 0, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac))/2a
where a = 1, b = 1, and c = -6. Therefore, the solutions are x = (-1 ± √(1 + 24))/2 = (-1 ± √25)/2 = (-1 ± 5)/2 = -3 or 2
So the solutions to the original equation are x = 1, -3 and 2
In general for x^3-ax^2-bx-c=0, one method to find the solutions is using polynomial roots that is factorisation. But it may also have complex solutions, it depends on the polynomial degree, the value of a,b,c.
если произведение равно нулю, то каждая скобочка равна нулюхотя бы одна из скобочек равна нулю
Так то да, но для понимания решения такие нюансы несущественны.
Мой запрос в chat gpt "x^3-7x+6=0 provide a solution".
Её ответ:
To solve the equation x^3 - 7x + 6 = 0, we can start by factoring the left-hand side of the equation.
One way to factor this equation is to factor out a greatest common factor (GCF) from the left-hand side. In this case, the GCF is 1, so we can write:
x^3 - 7x + 6 = (x-1)(x^2 + x - 6) = 0
Now we have a quadratic equation in the form of (x-1) (x^2 + x - 6) = 0. Using the zero product property, we know that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, either x-1 = 0 or x^2 + x - 6 = 0.
Solving for x-1 = 0, we find that x = 1.
To solve the quadratic equation x^2 + x - 6 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/2a
where a = 1, b = 1, and c = -6.
Therefore, the solutions are
x = (-1 ± √(1 + 24))/2 = (-1 ± √25)/2 = (-1 ± 5)/2 = -3 or 2
So the solutions to the original equation are x = 1, -3 and 2
In general for x^3-ax^2-bx-c=0, one method to find the solutions is using polynomial roots that is factorisation. But it may also have complex solutions, it depends on the polynomial degree, the value of a,b,c.