If a = 0.1 + $$\sqrt{0.9}$$​ and b = 0.1 - $$\sqrt{0.9}$$​ then what will be the value of $$\text{a}^2+\text{b}^2$$​?

Correct option is B

Given:

​$$a = 0.1 + \sqrt{0.9}$$​​

​$$b = 0.1 - \sqrt{0.9}$$​​

Formula Used:

​$$a^2 + b^2 = (a + b)^2 - 2ab$$​​

Solution:

$$ab = (0.1 + \sqrt{0.9})(0.1 - \sqrt{0.9}) = (0.1)^2 - (\sqrt{0.9})^2 = 0.01 - 0.9 = -0.89$$​​

$$a + b = (0.1 + \sqrt{0.9}) + (0.1 - \sqrt{0.9}) = 0.1 + 0.1 = 0.2$$​

​$$a^2 + b^2 = (a + b)^2 - 2ab = (0.2)^2 - 2(-0.89)$$​​

​$$a^2 + b^2 = 0.04 + 1.78 = 1.82$$​