Question

If x = 3 + √5, then find the value of x2 + 1.

Answer 1

Answer:

x =3+√5

(x+1) = (3+√5 +1)

Squaring both sides

(x+1)² = (4+√5)²

x²+1+2x = 16+5+8√5

x²+1 = 21+8√5-2x

x²+1= 21+8√5-2(3+√5)

x²+1= 21+8√5-6+2√5

x²+1= 15+(8√5+2√5)

x²+1=15+2√5(4+1)

x²+1=15+2√5×5

x²+1=15+10√5

OR

x²+1=5(3+2√3)