Question

10аб+(-5а+б)^2 при а = корень 2, б = корень 5

Answer 1

10аб+(-5а+б)^2 = 10ab+25a2-10ab+b2=25*a2+b2; подставляем значения: 25*10+5=255

Answer 2

To evaluate the expression 10аб + (-5а + б)^2 with the given values а = √2 and б = √5, follow these steps:

Step 1: Substitute the given values of а and б into the expression. Step 2: Perform the operations according to the order of operations (PEMDAS/BODMAS).

Let's start:

Step 1: Substitute the values а = √2 and б = √5 into the expression:

10 * √2 * √5 + (-5 * √2 + √5)^2

Step 2: Perform the operations:

10 * √2 * √5 = 10 * √(2 * 5) = 10 * √10

Now let's deal with the square term (-5 * √2 + √5)^2:

(-5 * √2 + √5)^2 = (-5 * √2 + √5) * (-5 * √2 + √5) = 25 * 2 - 5 * 2√10 - 5 * 2√10 + √5 * √5 = 50 - 10√10 - 10√10 + 5 = 55 - 20√10

Now we have:

10 * √10 + (55 - 20√10)

Step 3: Combine like terms:

The expression cannot be further simplified since the terms involving square roots (like √10) cannot be combined with the other terms.

So, the final expression is:

10√10 + 55 - 20√10

We can also combine the terms with the same radical (√10):

= (10√10 - 20√10) + 55

= -10√10 + 55

Thus, the simplified expression is -10√10 + 55 when а = √2 and б = √5.