MHB How Can You Solve for y in the Equation $(a+b)^{a+b} = a^a + y$?

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To solve for y in the equation (a+b)^{a+b} = a^a + y, the expression for y can be derived as y = (a+b)^{a+b} - a^a. This formulation allows for y to be expressed directly in terms of known values a and b. The discussion clarifies the relationship between the variables and the equation's structure. The proposed solution is straightforward and effectively isolates y. Understanding this relationship is crucial for further mathematical exploration.
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$$(a+b)^{a+b}=a^a+y$$ ; sorry i am edited a^b to a^a
Suppose we know a and b.
y in the term of a, b?
 
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How about
$$y=(a+b)^{a+b}-a^b? $$
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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