List of top Quantitative Aptitude Questions on Algebraic Identities asked in CAT

If \( x + \frac{1}{x} = 2 \), find the value of \( x^{10} + \frac{1}{x^{10}} \).
If x + y = 10 and xy = 21, what is x2 + y2?
If \(x=a^2+1\ \text{and} \ y=a^2-a+1\), then find the value of \(\frac{x^3-y^3-xy^2+x^2y}{(x+y)^2}\)