Variables and mathematical induction

Reference no: EM13119039

1) Prove that in the equation x^2 - 3xy +2y^2 - 2x - 3y - 35 = 0, for every real value of y there is a real value of x, and for every real value of x there is a real value of y.

2) Use the Principle of Mathematical Induction to prove:

a) For every positive integer n, 4^(2n + 1) + 3^(n+2) is a multiple of 13.

b) 3^n > n^2 for n >= 1

3) Prove that if 3 is a multiple of b^2 then 3 is also a multiple of b.

Reference no: EM13119039

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