Pls solve

If (s-a) + (s-b)+(s-c)=s then the value of

(s-a)² + (s-b)² +(s-c)²/(a)²+(b)²+(c)² is????

To solve the equation you've provided, we start by analyzing the expression and the condition you've given. The relationship (s - a) + (s - b) + (s - c) = s can be quite revealing, as it allows us to find the values of s in terms of a, b, and c.

Breaking Down the Equation

First, let's rewrite the given equation:

(s - a) + (s - b) + (s - c) = s

This simplifies to:

3s - (a + b + c) = s

Now, rearranging this gives us:

3s - s = a + b + c

Which simplifies to:

2s = a + b + c

So, we can express s as:

s = (a + b + c) / 2

Calculating the Required Expression

Now, we need to evaluate the expression:

(s - a)² + (s - b)² + (s - c)² / (a² + b² + c²).

We first need to determine the values of (s - a), (s - b), and (s - c). By substituting s:

• (s - a) = (a + b + c)/2 - a = (b + c - a)/2
• (s - b) = (a + b + c)/2 - b = (a + c - b)/2
• (s - c) = (a + b + c)/2 - c = (a + b - c)/2

Squaring Each Term

Next, we need to square each of these terms:

• (s - a)² = [(b + c - a)/2]² = (b + c - a)² / 4
• (s - b)² = [(a + c - b)/2]² = (a + c - b)² / 4
• (s - c)² = [(a + b - c)/2]² = (a + b - c)² / 4

Summing These Squares

Now we can sum these squared terms:

(s - a)² + (s - b)² + (s - c)² = [(b + c - a)² + (a + c - b)² + (a + b - c)²] / 4

Substituting Back

So, the entire expression we need is:

[(b + c - a)² + (a + c - b)² + (a + b - c)²] / 4 / (a² + b² + c²)

For simplification, we need to remember that the numerator represents a certain symmetrical property of a, b, and c.

Final Expression and Value

After careful consideration, it turns out that the numerator simplifies to (a² + b² + c² - ab - ac - bc). This is a known result that emerges from the squares of differences. Therefore, our expression can be rewritten as:

[(a² + b² + c² - ab - ac - bc) / 4] / (a² + b² + c²)

Final Result

Upon simplifying, we find:

Value = (1/4) * [1 - (ab + ac + bc) / (a² + b² + c²)]

This is a general form that depends on the specific values of a, b, and c, but gives a clear idea of how to approach similar problems.

In most cases, if we assume a, b, and c are equal, this expression simplifies further to 1/4, but variations will yield different results based on the particular values.