Question

Given p = 4q - r. Express q in terms of p and r

Answer 1

Answer:

The middle term in the square of p is a constant independent of x. This is good because the end terms will be equal to q. I.e.

[math]p^2 = (x - \frac{1}{x})^2 = x^2 -2(x)(\frac{1}{x}) + \frac{1}{x^2} = x^2 + \frac{1}{x^2} - 2[/math]

The first two terms are just q so just substitute it in to get the relation:

[math]p^2 = q -2 [/math]or [math]q=p^2+2[/math]

As a general rule, I think it’s useful to take note when the expression is in the form of x with its reciprocal. Taking powers of the term usually leads to cancellations of middle terms in the binomial expansion.

Practice and experience doing similar problems also help. These sort of problems where you are trying to get rid of one variable and express p directly in terms of q will come up quite often in parametric equations and is a useful skill to have.

Answer 2

Answer:

p=4q-r

or, 4q-r=p

or, 4q= p+r

or, q= (p+r)/4

Hope this will help you

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