Carcass wrote:
When \(a=x+(\frac{1}{x})\) and \(b=x-(\frac{1}{x})\), what is \(a^2 – b^2\)?
\(A. x^2 + \frac{1}{x^2}\)
\(B. x^2 - \frac{1}{x^2}\)
\(C. 1\)
\(D. 2\)
\(E. 4\)
Given: a =
x + 1/x and b =
x - 1/xOur goal is to find the value of a² - b²
To do so, it's useful to recognize that the expression a² - b² is a
difference of squares, which means we can rewrite it.
When we do this, we get: a² - b² = (a + b)(a - b)
Now replace a and b with their equivalent expressions to get: a² - b² = [(
x + 1/x) + (
x - 1/x)][(
x + 1/x) - (
x - 1/x)]
Simplify to get: a² - b² = [2x][2/x]
Simplify more to get: a² - b² = 4
Answer: E
Cheers,
Brent