If a = 5 + √6, b = 5 - √6, then what is the value of a² + b²?

Given:
a = 5 +$$\sqrt{6}$$​​
b = 5 - $$\sqrt{6}$$​​
Formula Used:
​$$(x + y)^2 = x^2 + y^2 + 2xy$$​​
​$$(x - y)^2 = x^2 + y^2 - 2xy$$​​
Solution:
First, calculate the square of a:
​$$a^2 = (5 + \sqrt{6})^2 = 25 + 6 + 10\sqrt{6} = 31 + 10\sqrt{6}$$​​
Next, calculate the square of b:

​$$b^2 = (5 - \sqrt{6})^2 = 25 + 6 - 10\sqrt{6} = 31 - 10\sqrt{6}$$​​
Now, add the two squared values together:
​$$a^2 + b^2 = 31 + 10\sqrt{6} + 31 - 10\sqrt{6}$$​​
$$a^2 + b^2$$​ = 62
Final Answer
So the correct answer is (c)