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First, let's think of how many different possibilities we have to seat 6 people at a 'normal' table, i.e. in a straight line. Let's call the people A, B, C, D, E, F. We now have 6 seats:

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(bx+d)(bx-d)=b^2x^2-d^2(ax-c)(bx+d)(bx-d)=(ax-c)(b^2x^2-d^2)=ab^2x^3-ad^2x-b^2cx^2+cd^2ab^2=3b^2c=2ad^2=147-cd^2=98From equations:a=3/b^2c=2/b^2d^2=49b^2Since a, b, c, d are positive integers, b must be 1...

We don't know what type of a triangle we're considering here. Therefore the universal and quickest solution to the first problem is use of the cosine rule, which states that for a triangle with sides a,b ...

When it comes to answering questions about inequalities, it is important to remember the signs and what they represent. In this instance, we need to find a range of solutions where 2(3x+1) is grea...