If a+(1/a) = 4 then a^2+(1/a^2)= ?

Question

If a+(1/a) = 4 then a^2+(1/a^2)= ?

 

The result is 14, and it can be guessed without knowing that a=(sqrt(3)+2)^2 But how?

 

It has something to do with the sum of squares, but I can't put my finger on it.

Answer 1

a + 1/a = 4

a² + 2(a)(1/a) + (1/a)² = 16   square both sides

a² + 2 + (1/a)² = 16

a² + (1/a)² = 14