Question

A/b=5/8 НОК(a;b)-НОД(a;b)=78a+b-?​

Answer 1

Ответ:

a=10

b=16

Пошаговое объяснение:

a/b=5/8 => a=5k b=8k Тогда НОД(a,b)=k

HOK(a,b)=a*b/НОД(a,b)=5*8*k

5*8*k-k=39*k=78 => k=2

Answer 2

To find the value of $a + b$, given that $\frac{a}{b} = \frac{5}{8}$ and $\text{LCM}(a, b) - \text{GCD}(a, b) = 78$, you can use the properties of least common multiples (LCM) and greatest common divisors (GCD).

Let's start with the fact that $\frac{a}{b} = \frac{5}{8}$. This means that $a$ and $b$ share a common factor of $5$, and the ratio between $a$ and $b$ is $\frac{5}{8}$. You can represent $a$ as $5x$ and $b$ as $8x$ for some positive integer $x$.

Now, we have:

$$\text{LCM}(a, b) = \text{LCM}(5x, 8x) = 40x$$

$$\text{GCD}(a, b) = \text{GCD}(5x, 8x) = x$$

Given that $\text{LCM}(a, b) - \text{GCD}(a, b) = 78$, you can substitute the values:

$$40x - x = 78$$

Now, solve for $x$:

$$39x = 78$$

Divide both sides by 39:

$$x = \frac{78}{39} = 2$$

Now that you have found the value of $x$, you can find $a$ and $b$:

$$a = 5x = 5 \cdot 2 = 10$$

$$b = 8x = 8 \cdot 2 = 16$$

Finally, calculate $a + b$:

$$a + b = 10 + 16 = 26$$

So, $a + b = 26$.