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Start by moving all the terms to one side of the inequality. In this case it's easiest to move the 6x to the left hand side by subtracting 6x from both sides, so that you are left with x^3 + x^2 - 6x >...

first the definition of the rank of a matrix is "maximal number of linearly independent column vectors in the matrix"

then the question could be rephrased to " how many ind...

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...

The procedure of mathematical induction is as following:

Firstly prove the base case is true i.e. when n=1, the statement is true.

Then assume for some integer n=k the state...