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prove that (3x+1)^2 - (3x-1)^2 is a multiple of 4 for all positive integer values of x

(3x + 1)2 = 9x2 + 6x + 1 (3x - 1)2 = 9x2 - 6x + 1 (9x2 + 6x + 1) - (9x2 - 6x + 1) = 12x 12x/4 = 3x Therefore for all positive integers of ...

Answered by Katie J. Maths tutor
5944 Views

Differentiate the following function u = Cos(x3)

 u = Cos(x3)

To differentiate this function we will use the chain rule. Firstly we will set xto another variable name such as v. So now v = x3 . Lets differentia...

Answered by Serena B. Maths tutor
2844 Views

Prove that the sqrt(2) is irrational

To do this we will assume sqrt(2) is rational, a fraction, which means: 21/2 = m/n; m,n belong to integers. Also, m/n is an irreductible fraction

Answered by Joao C. Maths tutor
3056 Views

Expand and simplify 2(a + 3) + 5(a – 1)

Firstly we will start by expanding the brackets. We will do 2a + 23 for the first bracket,  then we will do 5a + 5(-1) for the second bracket which will give us 2a + 6 + 5a - 5. We will ...

Answered by Serena B. Maths tutor
4033 Views

Factorise and solve x^2 - 8x + 15 = 0

In order to solve a quadratic equation by factorisation you must first find the two numbers which add up to - 8 and multiply to get 15. We can do this by trial and error - first listing all of the pairs o...

Answered by Lucy M. Maths tutor
4013 Views

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