Question

(X-7)•(x^2-6)=x^2-7x

Answer 1

Объяснение:

$(x - 7)(x {}^{2} - 6) - x(x - 7) = 0$

$(x - 7)(x {}^{2} - 6 - x) = 0$

$x - 7 = 0$

$x = 7$

$x {}^{2} - 6 - x = 0$

$x = - 2$

$x = 3$

Answer 2

$(x-7)(x^{2} -6)=x^{2} -7x$

Рассмотри два случая :

1. x - 7 = 0         =>          x = 7

$(7-7)(7^{2} -6)=7^{2} -7*7$

$0*(49 -6)=49-49$

$0=0$

2. x - 7 ≠ 0        => x ≠ 7

$(x-7)(x^{2} -6)=x^{2} -7x | :(x-7)$

$\frac{x-7}{x-7} (x^{2} -6)=\frac{x(x-7)}{x-7}$

$(x^{2} -6) = x$

$x^{2} -x-6 = 0$

По теореме Виета :

$x_1 +x_2 = 1$

$x_1 *x_2 = -6$

------------------

$x_1 = 3$

$x_2 = -2$

Ответ : -2 , 3, 7

Answer 3

Let's solve the equation step by step:

(X - 7) * (X^2 - 6) = X^2 - 7X

First, distribute the terms on the left side of the equation:

X * (X^2 - 6) - 7 * (X^2 - 6) = X^2 - 7X

Now, distribute again:

X^3 - 6X - 7X^2 + 42 = X^2 - 7X

Now, move all terms to the left side of the equation:

X^3 - 7X^2 - 6X + 42 - X^2 + 7X = 0

Combine like terms:

X^3 - 8X^2 + 42 = 0

Now, this is a cubic equation. To solve for X, you can try to factor it or use numerical methods such as the Rational Root Theorem or a calculator to find approximate solutions. Factoring may not be straightforward, so you might need to use numerical methods to find the roots.

The Rational Root Theorem helps you identify potential rational solutions. The rational roots of the equation are all possible combinations of factors of the constant term (42) over factors of the leading coefficient (1). In this case, the potential rational roots are ±1, ±2, ±3, ±6, ±7, ±14, ±21, and ±42.

You can try these values one by one to see if any of them make the equation equal to 0. Once you find a root, you can use polynomial division or synthetic division to simplify the equation and find the other roots.

Alternatively, you can use numerical methods or graphing software to approximate the solutions if factoring or rational roots don't work easily.