Question

(√5-1)^2-(2√+1)^2 решите пожалуйста

Answer 1

(√5-1)^2-(√2+1)^2=5+1-2√5-(2+1+2√2)=6-2√5-3-2√2=3-2√5-2√2

Answer 2

Solving the Expression (√5-1)^2-(2√+1)^2

To solve the given expression (√5-1)^2-(2√+1)^2, we can start by simplifying the terms and then solving for the result.

First, let's simplify the expression step by step:

1. Simplify (√5-1)^2: - The square of a binomial expression can be expanded using the formula (a - b)^2 = a^2 - 2ab + b^2. - Applying this formula to the given expression, we get: - (√5-1)^2 = (√5)^2 - 2*(√5)*1 + 1^2 - (√5-1)^2 = 5 - 2√5 + 1 - (√5-1)^2 = 6 - 2√5

2. Simplify (2√+1)^2: - Similarly, applying the formula (a + b)^2 = a^2 + 2ab + b^2 to the given expression, we get: - (2√+1)^2 = (2√)^2 + 2*(2√)*1 + 1^2 - (2√+1)^2 = 4*5 + 4√ + 1 - (2√+1)^2 = 20 + 4√ + 1 - (2√+1)^2 = 21 + 4√

3. Substitute the Simplified Expressions Back: - Now, substituting the simplified expressions back into the original expression, we get: - (√5-1)^2-(2√+1)^2 = (6 - 2√5) - (21 + 4√ + 1) - (√5-1)^2-(2√+1)^2 = 6 - 2√5 - 21 - 4√ - 1 - (√5-1)^2-(2√+1)^2 = -16 - 6√5 - 1

4. Final Result: - Combining like terms, the final result is: - (√5-1)^2-(2√+1)^2 = -17 - 6√5

Therefore, the result of the expression (√5-1)^2-(2√+1)^2 is -17 - 6√5.