Question

(4 -√7)^ 2 +(4+√ 7) ^ 2.

Answer 1

16-8√7+7+16+8√7+7=32+14=46

Answer 2

To simplify the given expression $(4 - \sqrt{7})^2 + (4 + \sqrt{7})^2$, follow these steps:

Expand both squared terms: $(4 - \sqrt{7})^2 = 4^2 - 2 \cdot 4 \cdot \sqrt{7} + (\sqrt{7})^2 = 16 - 8\sqrt{7} + 7 = 23 - 8\sqrt{7}$ $(4 + \sqrt{7})^2 = 4^2 + 2 \cdot 4 \cdot \sqrt{7} + (\sqrt{7})^2 = 16 + 8\sqrt{7} + 7 = 23 + 8\sqrt{7}$

Now add the two expressions together: $(23 - 8\sqrt{7}) + (23 + 8\sqrt{7}) = 23 + 23 = 46$

So, $(4 - \sqrt{7})^2 + (4 + \sqrt{7})^2 = 46$.