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Assumption: If sqrt(2^n- 1) ∈ℕ , it means that there is a k ∈ ℕ such that (2^n-1) = k^2 ⇒ k is odd, so there is m ∈ ℕ such that (2^n-1)=(2m+1)^2 . By solving the equation we get 2^n= 4m^2+4m+2. We divide bot...

3x 2 + 4x + 3 = 6x + 4

An odd number can be expressed by the formula "2n + 1" where n stands for any integer. Therefore, the square of any odd number can be expressed as:(2n+1)^2 = (2n+1)(2n+1) = 4n^2 + 4n + 1 = 4(n^2 + ...

Make x the subject in the equation x+y=11(1). This will help us eliminate x in the second equation (2).x=11-y (3)Substitute (3) into (2)(11-y) 2 +y 2 =61Expanding the brackets and simplifying gives 2y 2 -22y...

Every mathematical function has a range and a domain. The range of a function is the set of possible outputs the function has. In this case, we know that our output (y) must be a positive number because if w...