Question

(3 - √2) (5 + √2) - (√2 - 1^2)

Answer 1

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

Answer 2

Let's simplify the expression step by step.

First, we can expand the first part using the distributive property:

(3 - √2) (5 + √2) = 3(5) + 3(√2) - √2(5) - √2(√2) = 15 + 3√2 - 5√2 - 2 = 13 - 2√2

Next, we can simplify the second part:

(√2 - 1)^2 = (√2 - 1)(√2 - 1) = √2(√2) - √2(1) - 1(√2) + 1(1) = 2 - 2√2 + 1 = 3 - 2√2

Finally, we can substitute these values back into the original expression and simplify further:

(3 - √2) (5 + √2) - (√2 - 1)^2 = (13 - 2√2) - (3 - 2√2) = 13 - 2√2 - 3 + 2√2 = 10

Therefore, the simplified expression is 10.