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Prove that any number of the form pq, where p and q are prime numbers greater than 2, can be written as the difference of two squares in exactly two distinct ways.

If we want to prove it, we need to prove every odd number can be expressed as the difference of two squares, which is very easy. Suppose this odd number to be 2n-1, then we can see 2n-1=n 2 -(n-1) 2 Then we ...
SL
Answered by Shibo L. • STEP tutor
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Solve this pair of simultaneous equations (1) 5x+2y=20 and (2) x+4y=13

To solve these equations, our aim is to find a value of x and a value of y that satisfy both equations at the same time. By satisfy we mean, if we plug our values in for x and y then the left hand side and r...
JH
Answered by Jenny H. • Maths tutor
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How do I differentiate y=(4+9x)^5 with respect to x?

The method we use to differentiate this form of equation is called the chain rule. The chain rule is dy/dx = dy/du x du/dx We can rememeber the right way up of the terms on the right hand side by treating th...
JH
Answered by Jenny H. • Maths tutor
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Solve the simultaneous equations 2x+2y=14 and 3x-y=1

To solve these eliminations, we must eliminate either the x's or the y's. Either is possible but let us start with the y's. There is 2y in the first equation and (-1)y in the second, so we will have to multi...
AS
Answered by Angus S. • Maths tutor
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Find the solution(s) of 3(x^2)-6x+2=0

This is a quadratic equation and as such it has zero, one or two solutions depending on the value of the discriminant (b 2 -4ac). In this equation, a=3, b=-6 and c=2 so b 2 -4ac = 36-24=12. As this is >0 ...
AS
Answered by Angus S. • Maths tutor
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