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Maths
GCSE

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
5815 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
2960 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
3864 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
3851 Views

Solve 3x^2 - 4x - 6 = 0.

The at first can seem very challenging and you won't be able to tackle this question quickly using simple factorisation, which you can often do for many questions. It is best in this case then to use the ...

Answered by Aodhan B. Maths tutor
3660 Views

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