Question

1)(√19+√6)(√19-√6)+2,5= 2)(√7+√5)²-12= 3)(√9-4√5+√9+4√5)²=

Answer 1

Ответ:

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Answer 2

Let's simplify each of these expressions:

1. (√19+√6)(√19-√6) + 2.5:

Using the difference of squares formula (a^2 - b^2 = (a + b)(a - b)), we can simplify this expression:

(√19+√6)(√19-√6) = (√19)^2 - (√6)^2 = 19 - 6 = 13

Now, add 2.5 to this result:

13 + 2.5 = 15.5

So, the value of the first expression is 15.5.

2. (√7+√5)² - 12:

First, expand the square of the binomial:

(√7+√5)² = (√7+√5)(√7+√5) = (√7)^2 + 2(√7)(√5) + (√5)^2 = 7 + 2√35 + 5 = 12 + 2√35

Now, subtract 12 from this result:

(12 + 2√35) - 12 = 2√35

So, the value of the second expression is 2√35.

3. (√9-4√5+√9+4√5)²:

Simplify the terms inside the parentheses first:

(√9-4√5+√9+4√5) = (√9 + √9) + (-4√5 + 4√5) = 3√9 + 0 = 3(√9) = 3(3) = 9

Now, square this result:

9² = 81

So, the value of the third expression is 81.