If (4x – 7y) = 11 and xy = 8, what is the value of given that x and y are positive numbers?

If x + $$\frac 1x$$​= –1, then compute: $$x^4 + \frac{1}{x^4} + 2x^2 + \frac{2}{x^2}$$​​

​$$\text{Simplify: } 4\left(\frac{7}{4}x^2 - 27x + 19\right) - 7(x^2 + 9x - 14)$$​​

​$$\text{If } x - \frac{1}{x} = 3, \text{ then the value of } x^4 + \frac{1}{x^4} \text{ is:}$$​​

​$$\text{Simplify} \\\frac{8x^3 + 27y^3 - 64z^3 + 72xyz}{4x^2 + 9y^2 + 16z^2 - 6xy + 12yz + 8zx}$$​​

If $$x - \frac{1}{x} = 4$$, then the value of $$x^3 - \frac{1}{x^3}$$ is:​

If $$x - \frac{1}{x} = 10$$, then the value of $$x^3 - \frac{1}{x^3}$$ is:​

Simplify the following.
(2x +3)² − (x + 1)².

If  $$a^2+b^2 = 90$$​ and ab = 27, then find the possible value of $$\frac{a+b}{a-b}.$$​​

​$$\text{If }x + \frac{ 1}{x} = 17 \text{ then }x^2 + \frac{ 1}{x^2} \text{ is:}$$

If a + b = 41, and a − b = 38, find the value of (a + b)².