Question

(3+√5)(5-√5)-(√5+1)в степени 2

Answer 1

Ответ:

4

Объяснение:

$(3+\sqrt{5} )(5-\sqrt{5})-(\sqrt{5}+1):2=15-3\sqrt{5}+5\sqrt{5}-5-6-2\sqrt{5}=4$

Answer 2

To simplify the expression, let's start by expanding each term step by step:

Step 1: Expand (3 + √5)(5 - √5) Using the FOIL method (First, Outer, Inner, Last), we get: = 3 * 5 + 3 * (-√5) + √5 * 5 - √5 * (-√5) = 15 - 3√5 + 5√5 + 5 = 20 + 2√5

Step 2: Now, we have (20 + 2√5) - (√5 + 1) squared. To square a binomial, we use the formula: (a - b)^2 = a^2 - 2ab + b^2

So, in our case: = (20 + 2√5)^2 - 2(20 + 2√5)(√5 + 1) + (√5 + 1)^2

Step 3: Simplify each term within the squared expression: = (20 + 2√5)(20 + 2√5) - 2(20 + 2√5)(√5 + 1) + (√5 + 1)(√5 + 1) = 400 + 40√5 + 40√5 + 4(√5)^2 - 40√5 - 4 - 2(√5 + 1) + (√5)^2 + 2√5 + 1 (Note: (√5)^2 = 5)

Step 4: Simplify further: = 400 + 80√5 + 20 - 40√5 - 4 - 2√5 - 5 + 2√5 + 1 = 416 + 2√5 - 5 = 411 + 2√5

So, the simplified expression is: 411 + 2√5.