If a = 7 + √2, b = 7 - √2, then what is the value of a² + b²?

Correct option is C

Given:
a = $$7 + \sqrt{2}$$​​
b = $$7 - \sqrt{2}$$​​
Formula Used:
​$$(a + b)^2 + (a - b)^2 = 2 × (a^2 + b^2)$$​​
Solution:
We need to find the value of $$a^2 + b^2.$$​​
Substitute the given values into the algebraic identity format directly.
​$$(7 + \sqrt{2})^2 + (7 - \sqrt{2})^2$$ 

$$= 2 × (7^2 + (\sqrt{2})^2)$$ 

= 2 ×( 49 + 2) 

= 2 × 51

= 102
Final Answer
So the correct answer is (c)