Question

if a= 3+√5/2 find a^2+1/a^2​

Answer 1

First find the reciprocal.

$a=\frac{3+\sqrt{5} }{2}$ ∴ $\frac{1}{a} =\frac{2}{3+\sqrt{5} } =\frac{2(3-\sqrt{5}) }{4} =\frac{3-\sqrt{5} }{2}$

Their sum is 3, it becomes so simple.

There is an algebraic identity.

(x+y)²=x²+2xy+y²

If we put a and 1/a into x and y

(a+1/a)²=a²+2+1/a²

Therefore we get a²+1/a²=(a+1/a)²-2

a²+1/a²=3²-2=7

Therefore, the value is 7.

Answer 2

Answer:29root2/2 +2/29root2

Step-by-step explanation:

a^2=9+5/2+2×3×root5/2

a^2=23/2+6root5/root2×root2/root 2

a^2=23/2+6root10/2

a^2=29root2/2

a^2+1/a^2=29root2/2 + 2/29root2