Question

(3-sqrt2)(5+sqrt2) - (sqrt2 - 1)^2 (полное решение)

Answer 1

$\tt(3-\sqrt{2})(5+\sqrt{2})-(\sqrt{2}-1)^2=\\\\=15+3\sqrt{2}-5\sqrt{2}-2-(2-2\sqrt{2}+1)=\\\\=13-2\sqrt{2}-2+2\sqrt{2}-1=10$

Answer 2

Let's first simplify the expression using the distributive property of multiplication:

(3 - sqrt(2))(5 + sqrt(2)) - (sqrt(2) - 1)^2 = 3(5) + 3(sqrt(2)) - sqrt(2)(5) - (sqrt(2))^2 - (sqrt(2) - 1)^2 = 15 + 3sqrt(2) - 5sqrt(2) - 2 - 2sqrt(2) + 1 = 14 - 4sqrt(2)

Therefore, the simplified expression is 14 - 4sqrt(2).