Question

(3×+17):2= НОД(770;1190)​

Answer 1

(3×+17):2= НОД(770;1190)         770 = 2•5•7•11       1190 = 2•5•7•17

(3×+17):2=70                               НОД (770, 1190) = 2*5*7 = 70

(3×+17)=70*2

(3×+17)=140

3x=140-17

3x=123

x=123:3

x=41

Ответ: x=41

Answer 2

To find the value of x in the equation (3× + 17)/2 = GCD(770, 1190), we need to calculate the greatest common divisor (GCD) of 770 and 1190.

The prime factorization of 770 is 2 * 5 * 7 * 11, and the prime factorization of 1190 is 2 * 5 * 7 * 17.

To calculate the GCD, we take the highest power of each common prime factor between the two numbers. In this case, the highest power of 2 is 2^1, the highest power of 5 is 5^1, the highest power of 7 is 7^1, and the highest power of 17 is 17^1.

Therefore, GCD(770, 1190) = 2 * 5 * 7 * 17 = 1190.

Now we can substitute the value of GCD(770, 1190) back into the original equation:

(3x + 17)/2 = 1190

To isolate x, we can multiply both sides of the equation by 2:

3x + 17 = 2380

Next, we subtract 17 from both sides:

3x = 2363

Finally, divide both sides by 3:

x = 2363/3 ≈ 787.67

Therefore, the value of x in the equation (3× + 17)/2 = GCD(770, 1190) is approximately 787.67.