If x = 2 + √5 and y = 2 - √5, then the value of $$x^2+y^2$$​ is:

Correct option is C

Given:

x $$=2+\sqrt5$$

y = $$2−\sqrt5$$

Solution:

Calculate $$x^2$$ :

​$$x^2 = (2+ \sqrt5)^2$$ = $$2^2 + 2 . 2.\sqrt5 +(\sqrt5)^2$$​​

​​$$x^2 = 4+4\sqrt5+5$$​​

​​$$x^2 = 9+4\sqrt5$$

​​Calculate $$y^2$$:

​​$$y^2 = (2-\sqrt5)^2=$$ $$2^2 -2.2.\sqrt5+(\sqrt5)^2$$

$$y^2 = 4-4\sqrt5+5$$

$$y^2 = 9-4\sqrt5$$

$$\text{ Now,} \quad x^2+y^2$$ :

​$$x^2+y^2$$ = $$( 9+4\sqrt5 )$$ + $$(9-4\sqrt5)$$

​​$$x^2+y^2$$ = $$9+9 +4\sqrt5-4\sqrt5$$

$$x^2+y^2$$ = 18

Therefore, the value of $$x^2+y^2$$ is 18

Thus, correct answer is (c) 18