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How do I rationalise the denominator of √2+1]/√2-1?

We must choose something to multiply the numerator and denominator of the fraction by the same thing, and the best thing to choose is the difference of two squares (since (x^2-y)(x^2+y)=x^2-y^2 ). So we do (...
HJ
Answered by Harry J. • Maths tutor
6249 Views

Why is there more than one solution to x^2 = 4?

Think about it as 'What numbers can be x to get 4'. Remember that when you square a number the answer is always positive? Here is a situation in which it's important to consider both of the possible solution...
BT
Answered by Benjamin T. • Maths tutor
4114 Views

How do you show some quadratic polynomials are always greater than 0?

Usually, there are two ways to solve this kind of problems. You could re-arrange the polynomial, make it become a square plus a constant, then the polynomial is greater or equal to the constant since a squar...
LW
Answered by Luke W. • Maths tutor
6854 Views

Differentiate the function y=4sqrt(x)

Can re-write function as y=4x 1/2 Then follow the standard steps for differentiating a power. Take the 1/2 down and multiply by the number in front of the x, in this case 4, to give 2. Now reduce the power w...
CW
Answered by Calum W. • Maths tutor
3773 Views

A cuboid has dimensions: width = x+1, length = 2x-2, height = x+2. Work out the volume of this cuboid. Give your answer in terms of x.

Volume of cuboid = width x length x heightV = (x + 1)(2x - 2)(x + 2) For simplicity, multiply the first 2 sets of brackets first. Then multiply the result by the third set of brackets.Note: for multiplicatio...
SA
Answered by Sam A. • Maths tutor
6855 Views