Question

(13-√17)(13+√17)+(4-3 √5)^2

Answer 1

(13-√17)(13+√17)+(4-3√5)²=(169-17)+(16-24√5+45)=169-17+16-24√5+45=213-24√5

Answer 2

Let's break down the expression step by step:

1. (13 - √17)(13 + √17): This expression represents the difference of squares. We can use the formula (a - b)(a + b) = a^2 - b^2 to simplify it.

Applying the formula, we have: (13 - √17)(13 + √17) = 13^2 - (√17)^2 = 169 - 17 = 152

2. (4 - 3√5)^2: To simplify this expression, we need to expand it using the formula (a - b)^2 = a^2 - 2ab + b^2.

Expanding (4 - 3√5)^2, we have: (4 - 3√5)^2 = (4^2) - 2(4)(3√5) + (3√5)^2 = 16 - 24√5 + 9(5) = 16 - 24√5 + 45 = 61 - 24√5

Now, let's add the two simplified expressions together:

152 + (61 - 24√5) = 213 - 24√5

Therefore, the final simplified expression is 213 - 24√5.