If a^2-3a + 1 = 0, (a\ne 0 ), then the value of a^2 + \dfrac{1}{a^2} is

If a^2−4a−1=0,a≠0, then the value of a^2+3a+\dfrac{1}{a^2}-\dfrac{3}{a} is

If a is a root for the following equation

x^2+\sqrt{3}x-2 = 0

Find the value of

\dfrac{a^4}{a^8+a^6+2a^4+4a^2+16}

Find the value of 12 to the power of (1+sqrt(5))/2

\Big( \dfrac{\sqrt{5}+1 }{2}\Big) ^{12}

If x^n+\dfrac{1}{x^{2n}}=1 , find the value of the polynomial x^{5n}+x^n+2

Given x^2-3x+1=0 , find the value of the expression x^2+\dfrac{1}{x^2} , x^3+\dfrac{1}{x^3} and x^4+\dfrac{1}{x^4}