Question

if x=(2+√5)^1/2+(2-√5)^1/2 and y=(2+√5)^1/2-(2-√5)^1/2

Answer 1

Answer:

Using the maths property:

(a+b)(a-b) = a^{2}-b^{2}a

2

−b

2

;

x = (2+√5)1/2+(2-√5)1/2

Taking 1/2 as common;

x = (1/2) [(2+√5)+(2-√5)] = (1/2) [2+2];

x = 2;

y = (2+√5)1/2-(2-√5)1/2;

Taking 1/2 as common;

y = (1/2) [2+√5 - 2+√5]

y = (1/2) [2√5] = √5;

x^2+y^2 = 4+5 = 9