MHB Exponential Equation: If X is one more than twice Y, what is the value of X?

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The discussion revolves around solving the equation where the square of X equals four times the square of Y, and X is defined as one more than twice Y. The equation X^2 = 4Y^2 leads to two potential solutions for X: X = 2Y or X = -2Y. By substituting these values into the equation X = 2Y + 1, users are prompted to explore the outcomes of each substitution. The goal is to determine the specific value of X based on these relationships. The discussion emphasizes the importance of showing progress to facilitate better assistance.
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The square of X is equal to 4 times the square of Y. If X is one more than twice Y, what is the value of X?
 
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Hello and welcome to MHB, ScrewedIre! (Wave)

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ScrewedIre said:
The square of X is equal to 4 times the square of Y.
X^2= 4Y^2
Do you see that either X= 2Y or X= -2Y?

If X is one more than twice Y
X= 2Y+ 1

If you replace X with 2Y what do you get? If you replace X with -2Y what do you get?

, what is the value of X?
 

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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