[tex]\it a)\ \ x^2-y^2=(x-y)(x+y)=2\cdot3=6\\ \\ b)\ \ x^2+y^2=(x+y)^2-2xy=6^2-2\cdot4=36-8=28\\ \\ \\ f)\ \ \Big(x+\dfrac{1}{x}\Big)^2=x^2+2\cdot x\cdot\dfrac{1}{x}+\dfrac{1}{x^2}=x^2+\dfrac{1}{x^2}+2 \Rightarrow \\ \\ \\ \Rightarrow x^2+\dfrac{1}{x^2}=\Big(x+\dfrac{1}{x}\Big)^2-2=2^2-2=4-2=2\\ \\ \\ x^4+\dfrac{1}{x^4}=\Big(x^2+\dfrac{1}{x^2}\Big)^2-2=2^2-2=2[/tex]
