Question

2a=bc, 3b=ac,4c=ab, a²+b²+c²=?

Answer 1

Ответ:

26

Пошаговое объяснение:

Answer 2

Let's solve the given system of equations to find the values of a, b, and c, and then calculate a² + b² + c².

We have the following equations:

1. 2a = bc
2. 3b = ac
3. 4c = ab

Let's solve these equations step by step:

From equation 1, we can express c in terms of a: c = 2a/b.

Substituting this value of c into equation 2, we have:

3b = a(2a/b) 3b = 2a²/b 3b² = 2a²

Now, substituting c = 2a/b into equation 3:

4(2a/b) = ab 8a/b = ab 8a = ab²

Dividing equation 3 by equation 2, we get:

(8a)/(3b²) = (ab²)/(2a²) 8/(3b²) = b/a

Now, let's solve these two equations together:

From the equation (8a)/(3b²) = b/a, we can cross-multiply:

8a² = 3b³

Rearranging equation 3b² = 2a² as 2a² = 3b², we have:

4a² = 6b²

Dividing 8a² = 3b³ by 4a² = 6b², we get:

(8a²)/(4a²) = (3b³)/(6b²) 2 = (1/2)b

b = 4

Substituting the value of b = 4 into equation 4c = ab, we have:

4c = a(4) 4c = 4a c = a

Now, substituting b = 4 and c = a into equation 2a = bc, we get:

2a = 4a 2 = 4

Since 2 = 4 is not true, there is no solution to the given system of equations. Therefore, we cannot calculate the value of a² + b² + c².