MHB Given a quadratic in x, find the cube of x

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To find \( x^3 \) given \( x^2 = x + 3 \), one can first rearrange the equation to form \( x^2 - x - 3 = 0 \) and apply the quadratic formula. Once the values of \( x \) are determined, \( x^3 \) can be calculated using the relationship \( x^3 = x \cdot x^2 \). Substituting \( x^2 \) from the original equation into this expression simplifies the calculation. The final result for \( x^3 \) can be derived directly from these steps.
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if $x^2 = x+3$ then $x^3 = ??$ Not sure about this would appreciate some help
 
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Assuming that your question is the following:

If $x^2=x+3$, then find $x^3$

Here, we need to find what $x$ is, and to do so, we can apply the quadratic formula on $x^2-x-3=0$
 
Rido12 said:
Assuming that your question is the following:

If $x^2=x+3$, then find $x^3$

Here, we need to find what $x$ is, and to do so, we can apply the quadratic formula on $x^2-x-3=0$

Thanks a lot have got it
 

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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