Question

(x-2)(x+2)-x(x-13) при x = -2/13

Answer 1

$x { }^{2} - 4 - x {}^{2} + 13x \\ - 4 + 13x \\ \times = - \frac{2}{13 } \\ 13 \times ( - \frac{2}{13}) = - 2 - 4 = - 6$

Answer 2

$x ^2 - 4 - x ^{2} + 13x \\ - 4 + 13x \\ - 4 + 13 \times - \frac{2}{13} \\ = - 6$

Answer 3

To evaluate the expression (x-2)(x+2)-x(x-13) at a specific value of x, which is x = -2/13, we simply substitute -2/13 in place of x and perform the calculations.

Let's do the math step by step:

1. Replace x with -2/13 in the expression: ((-2/13)-2)((-2/13)+2) - (-2/13)((-2/13)-13)

2. Simplify each term: ((-2/13)-2) = (-2/13-26/13) = -28/13 ((-2/13)+2) = (-2/13+26/13) = 24/13 ((-2/13)-13) = (-2/13-169/13) = -171/13

3. Now the expression becomes: (-28/13) * (24/13) - (-2/13) * (-171/13)

4. Perform the multiplication: (-28/13) * (24/13) = -672/169 (-2/13) * (-171/13) = 342/169

5. Now the expression becomes: -672/169 - 342/169

6. Combine the fractions: (-672 - 342)/169 = -1014/169

So, the value of the expression (x-2)(x+2)-x(x-13) at x = -2/13 is -1014/169.