Question

(b^2 - 8ab)\(b^2 - 64a^2) при а=корень из 2. b=корень из 8.

Answer 1

В принципе, можно упростить:
$\dfrac{b^2 - 8ab}{b^2 - 64a^2}=\dfrac{b(b-8a)}{(b-8a)(b+8a)}=\dfrac{b}{b+8a}$
т.к. b = 2a, получаем

2a / (2a + 8a) = 2/10 = 0.2

Answer 2

(b^2 - 8ab)\(b^2 - 64a^2) =b(b - 8a)\((b - 8a)(b+8a))=
=b\(b+8a))=корень(8)/(корень(8)+8*корень(2)) =
=2корень(2)/(2корень(2)+8*корень(2)) =
=1/(1+4) = 0,2

Answer 3

To find the value of $\frac{{(b^2 - 8ab)}}{{(b^2 - 64a^2)}}$ when $a = \sqrt{2}$ and $b = \sqrt{8}$, we can substitute these values into the expression:

$$\frac{{(\sqrt{8}^2 - 8 \cdot \sqrt{8} \cdot \sqrt{2})}}{{(\sqrt{8}^2 - 64 \cdot \sqrt{2}^2)}}$$

Simplifying the expression gives:

$$\frac{{(8 - 8 \cdot 2)}}{{(8 - 64 \cdot 2)}}$$

Further simplification yields:

$$\frac{{(8 - 16)}}{{(8 - 128)}}$$

$$\frac{{-8}}{{-120}}$$

Dividing both numerator and denominator by their greatest common divisor, which is 8, gives:

$$\frac{{-1}}{{15}}$$

Therefore, when $a = \sqrt{2}$ and $b = \sqrt{8}$, the value of $\frac{{(b^2 - 8ab)}}{{(b^2 - 64a^2)}}$ is $-\frac{1}{15}$.