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Solve the simultaneous equations: 4x+5y = 38 , x-y = 5

Firstly number the two equations 1 and 2 for simplicity. To solve this we want to eliminate one of the variables, x or y, so we start by looking at the equations and seeing if we can add or subtract them fro...
AA
Answered by Ali A. • Maths tutor
5037 Views

A common question would be how to factorise into two brackets, for example x^2 + 5x = -6

The first thing you must do is get all the terms on the same side, which we do by adding 6 to both sides : x^2 + 5x + 6 = 0. Next, we must work out which numbers add to the middle term, and write these down ...
MT
Answered by Madeleine T. • Maths tutor
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I don't understand the point of differentiation or integration

If thinking about graphs, differentiation is the gradient, and integration is the area between the line and the axis. These operations are useful if we know values that are related through them, for example ...
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Answered by Guido B. • Maths tutor
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Solve the inequality x(x+2)>8 for x.

x(x+2)>8 if and only if x^2+2x-8>0 if and only if (x+4)(x-2)>0. There are three cases: x<-4, -4 In the first case x+4<0 and x-2<0, so their product is positive: (x+4)(x-2)>0. Next x+4&gt...
JT
Answered by Joshua T. • Maths tutor
4812 Views

The quadratic equation 2x^2+8x+1=0 has roots a and b. Write down the value of a+b and ab and a^2+b^2.

Since the quadratic has roots a and b, this means it can be fatored as 2(x-a)(x-b)=0. Expanding this out we get 2x^2-2(a+b)x+2ab=0 and matching the coefficients for the terms x^1 and x^0 we get a+b=-4 and ab...
JT
Answered by Joshua T. • Maths tutor
5448 Views