Question

1) a+b=85, НСД(a,b)=102; 2) ab = 20, НСK(a,b)=10; 3) ab = 6, НСД(a,b)=1.

Answer 1

Ответ:

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Answer 2

To solve these equations, we'll need to find the values of 'a' and 'b' that satisfy the given conditions. Let's solve each equation step by step:

1. a + b = 85, GCD(a, b) = 102:

The greatest common divisor (GCD) of two numbers cannot be greater than the sum of the two numbers. Since the GCD is 102, which is greater than 85, there is no solution to this equation.

2. ab = 20, LCM(a, b) = 10:

The least common multiple (LCM) of two numbers cannot be smaller than their product. Since the LCM is 10, which is smaller than 20, there is no solution to this equation.

3. ab = 6, GCD(a, b) = 1:

To find the values of 'a' and 'b' that satisfy this equation, we need to consider the prime factors of 6, which are 2 and 3.

The possible combinations of 'a' and 'b' that multiply to 6 are: a = 1, b = 6 a = 2, b = 3 a = 3, b = 2 a = 6, b = 1

So, there are four solutions for this equation: (1, 6), (2, 3), (3, 2), and (6, 1).