MHB Solving Cubic Root Algebra: Don't Know the Steps

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The discussion centers around confusion regarding the steps to solve a cubic root algebra problem. The main point of contention is the assertion that "a is not supposed to be -1," which is highlighted as a critical rule in the equation. Participants express uncertainty about the validity of the equation leading to the answer shown in a referenced image. One user suggests that a typo may exist, particularly questioning the expression involving the cubic root of 0.125. Overall, clarity on the steps and correctness of the equation is sought.
STS
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I don't understand this.
a is not suppose to be -1; this is the only rule in the equation
The answer is the second picture, I just don't know the steps that lead to that answer.
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STS said:
I don't understand this.
a is not suppose to be -1; this is the only rule in the equation
The answer is the second picture, I just don't know the steps that lead to that answer.
In order for this to be correct we would need [math]\sqrt[3]{ 0.125 - 0.5 } = 0[/math], which clearly isn't true. Is there a typo?

-Dan
 
Hi STS.

You probably mean the following expression:
$$\frac{4a^2-10\times\sqrt[3]{0.064}}{3a+3+{\color{red}\sqrt[3]{0.125}}-0.5}.$$
 
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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