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Set the equations equal to each other: 4x^2 + 5x + 3 = x + 2Collect terms and set equal to 0: 4x^2 + 4x + 1 = 0Factorise the equation: (2x + 1)(2x + 1) = 0Can now find the value of x: 2x + 1 = 0, therefor...

First set the equations equal to each other: x^2+4x+4 = 2x+3.Rearrange for x in form ax^2+bx+c : x^2+2x+1=0Factorise: (x+1)^2=0. Repeated root, hence only one intersection. x=-1. Using y=2x+3, y=1. So coo...

(7 + √3)(7 - √3) = 7² + 7√3 - 7√3 - (√3)² = 49 - 3 = 46Alternatively you can go straight to identifying that this is the difference between two squares, using the fact that (a + b)(a...

y=3x+7 2y-6x=8
2y-6x=82y=8+6xy= 4+3xy=3x+4When both equations equal y they both have a 3 in front of their x meaning that they both have a gradient of 3.

To work out the total volume of the composite solid, we need the volumes of both the cone and the hemisphere. GCSE Maths students are expected to know these respective formulae; volume of a sphere = ⁴/₃πr...