A binary operation * is defined on the set of real numbers, R, by P * q = \(\frac{q^2 - p^2}{2pq}\). Find 3 * 2

Solve (\(\frac{1}{9}\))\(^{x + 2}\) = 243\(^{x - 2}\)

Simplify \(\frac{1}{3}\) log8 + \(\frac{1}{3}\) log 64 - 2 log6

In how many ways can 8 persons be seated on a bench if only three seats are available?

Using binomial expansion of ( 1 + x)\(^6\) = 1 + 6x + 15x\(^2\) + 20x\(^3\) + 6x\(^5\) + x)\(^6\), find, correct to three decimal places, the value of (1.998...

Simplify ( \(\frac{1}{2 - √3}\) + \(\frac{2}{2 + √3}\) )\(^{-1}\)

g(x) = 2x + 3 and f(x) = 3x\(^2\) - 2x + 4

Given that \( M = \begin{pmatrix} 3 & 2 \\ -1 & 4 \end{pmatrix} \) and \( N = \begin{pmatrix} 5 & 6 \\ -2 & -3 \end{pmatrix} \), calculate \( (3M - 2N) \)

For what range of values of x is x\(^2\) - 2x - 3 ≤ 0