Question

(3+√5)(5-√5)-(√5+1)^2

Answer 1

$(3+\sqrt5)(5-\sqrt5)-(\sqrt5+1)^2=15-3\sqrt5+5\sqrt5-5-5-2\sqrt5-1=4$

Answer 2

Это все равно (=) 4..............

Answer 3

To simplify the given expression, let's start by expanding it step by step:

Expression: (3 + √5)(5 - √5) - (√5 + 1)^2

Step 1: Expand (3 + √5)(5 - √5) Using the distributive property (FOIL method): = 3 * 5 + 3 * (-√5) + √5 * 5 + √5 * (-√5) = 15 - 3√5 + 5√5 - √5 * √5 (Note that √5 * √5 is simply 5, as the square root cancels out)

Step 2: Simplify √5 * √5 √5 * √5 = 5

Step 3: Combine like terms = 15 + (5 - 3)√5 - 5 = 10 - √5

Step 4: Expand (√5 + 1)^2 This is equivalent to (√5 + 1) * (√5 + 1) using the distributive property (FOIL method): = √5 * √5 + √5 * 1 + 1 * √5 + 1 * 1 = 5 + 2√5 + 1 = 6 + 2√5

Now, let's put it all together and simplify the expression:

Final expression: (3 + √5)(5 - √5) - (√5 + 1)^2 = (10 - √5) - (6 + 2√5)

Now, combine like terms: = 10 - √5 - 6 - 2√5

Combine the constant terms and the terms with √5: = (10 - 6) - (√5 + 2√5) = 4 - 3√5

So, the simplified expression is 4 - 3√5.