Answer:
The actual value of the breadth of the land is (3x² - 102x + 786) / (x-17)².
Explanation:
Finding the total area of the rectangular land. The area can be calculated by multiplying the length and the breadth of the land. Let the breadth of the land be 'b' units.
So, the total area of the rectangular land is:
Length × Breadth = (x-17) × b
We know that the area received by the first son is x²-9 square units, the area received by the second son is x² + 2x-15 square units, and the area received by the third son is x²-6x +9 square units.
According to the problem, the sum of the areas received by the three sons must be equal to the total area of the land. So, we can write an equation as follows:
x² - 9 + x² + 2x - 15 + x² - 6x + 9 = (x-17) × b
Simplifying this equation, we get:
3x² - 4x - 15 = (x-17) × b
Now, we know that x-17, so we can substitute this value in the above equation to get:
3x² - 4x - 15 = (x-17) × b
3x² - 4x - 15 = -b(17 - x)
3x² - 4x - 15 = b(x - 17)
Since we need to find the breadth of the land, we can isolate 'b' on one side of the equation and simplify:
b = (3x² - 4x - 15) / (x - 17)
Now, we can substitute the value of x-17 to get:
b = (3(x-5)(x+1)) / (x-17)
We can simplify this expression by canceling out the factor (x-17) in the numerator and denominator, which gives:
b = 3(x+1)/(x-17) × (x-5)/(x-17)
b = 3(x² - 4x - 5) / (x-17)²
Now, we can substitute the given value of x-17 to get the actual value of the breadth of the land:
b = 3((x-17)² - 4(x-17) - 5) / (x-17)²
b = 3(x-17)² - 12(x-17) - 15 / (x-17)²
b = (3x² - 102x + 786) / (x-17)²
Therefore, the actual value of the breadth of the land is (3x² - 102x + 786) / (x-17)².