Question

(√5-2)²-(√5-1)(√5-3)=

Answer 1

Ответ:

Объяснение:

Раскрываем скобки и приводим подобные

Answer 2

(√5-2)-(√5-1)(√5-3)=5-4-(5-3√5-√5+4)

=1-5+3√5+√5-4=4√5-8

Answer 3

Let's simplify the expression step by step:

1. Start with the first term: (√5 - 2)² Apply the square of a binomial formula: (a - b)² = a² - 2ab + b²

   In this case, a = √5 and b = 2: (√5 - 2)² = (√5)² - 2 * √5 * 2 + 2² = 5 - 4√5 + 4 = 9 - 4√5

2. Move on to the second term: (√5 - 1)(√5 - 3) Use the FOIL method to expand the expression: (√5 - 1)(√5 - 3) = √5 * √5 - √5 * 3 - 1 * √5 + 1 * 3 = 5 - 3√5 - √5 + 3 = 8 - 4√5

3. Substitute the simplified values back into the original expression: (√5 - 2)² - (√5 - 1)(√5 - 3) = (9 - 4√5) - (8 - 4√5) = 9 - 4√5 - 8 + 4√5 = 1

Therefore, the expression (√5 - 2)² - (√5 - 1)(√5 - 3) simplifies to 1.