MHB Basic Math - Learn the Basics of Mathematics

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The discussion focuses on simplifying a mathematical expression involving variables a, b, and c. The left-hand side is rewritten using the identity for the difference of squares, resulting in the equation (b+c)² - a² = λbc. The next step involves eliminating a² by applying the law of cosines, which expresses a² in terms of b, c, and the cosine of angle α. Participants are encouraged to fill in this substitution and simplify the resulting expression further. The conversation emphasizes foundational algebraic techniques and the application of trigonometric identities.
Ande Yashwanth
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Hi Ande Yashwanth! Welcome to MHB! (Smile)

First step would be to multiply out the left hand side.
Did you already do that?
Anyway, being smart about it, we can write the left hand side as:
$$(a+b+c)(b+c-a)=((b+c)+a)((b+c)-a)=(b+c)^2-a^2$$
So we get:
$$(b+c)^2-a^2=\lambda bc$$

Now we want to get rid of the $a^2$.
We can do so by applying the law of cosines:
$$a^2=b^2+c^2 - 2bc\cos\alpha$$
What would we get if we fill that in and simplify further? (Wondering)
 

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?
View full post »

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