Q&A If a is a root for the following equationx^2+\sqrt{3}x-2 = 0 Find the value of \dfrac{a^4}{a^8+a^6+2a^4+4a^2+16}

Q&A Let n be a rational number such that the equation x^2-(\sqrt{3}+1)x+\sqrt{3}n-6 = 0has an integer root. Find the value of n.

Q&A One of the roots of a quadratic equation x^2-(\tan \alpha+\cot \alpha )x+1 = 0 in terms of x is 2+\sqrt{3} . Evaluate \sin \alpha \cdotp \cos \alpha ,