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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 = 9x 2 + 6x + 1 (3x - 1) 2 = 9x 2 - 6x + 1 (9x 2 + 6x + 1) - (9x 2 - 6x + 1) = 12x 12x/4 = 3x Therefore for all positive integers of x the result is a multiple of 4
KJ
Answered by Katie J. • Maths tutor
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Prove that the sqrt(2) is irrational

To do this we will assume sqrt(2) is rational , a fraction, which means: 2 1/2 = m/n ; m,n belong to integers. Also, m/n is an irreductible fraction , meaning m and n have no common divisors. 2 1/2 = m/n &lt...
JC
Answered by Joao C. • Maths tutor
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Expand and simplify 2(a + 3) + 5(a – 1)

Firstly we will start by expanding the brackets. We will do 2 a + 2 3 for the first bracket, then we will do 5 a + 5 (-1) for the second bracket which will give us 2a + 6 + 5a - 5. We will then simplify what...
SB
Answered by Serena B. • Maths tutor
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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 of f...
LM
Answered by Lucy M. • Maths tutor
5696 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 Qua...
AB
Answered by Aodhan B. • Maths tutor
5226 Views