Question

Упростить: 0.96*(0.2^2+1)(0.2^4+1)(0.2^8+1)(0.2^16+1)(0.2^32+1)

Answer 1

это если в лёгком порядке и без ответа

Answer 2

To simplify the expression, we can start by factoring out the common factor of (0.2^2 + 1) from each term:

0.96 * (0.2^2 + 1) * (0.2^4 + 1) * (0.2^8 + 1) * (0.2^16 + 1) * (0.2^32 + 1)

= 0.96 * [(0.2^2 + 1) * (0.2^4 + 1) * (0.2^8 + 1) * (0.2^16 + 1) * (0.2^32 + 1)]

Now, let's notice a pattern in the terms inside the brackets. Each term is of the form (a^b + 1), where a = 0.2 and b = 2, 4, 8, 16, 32.

We know that (a^b + 1) is a sum of squares, and it can be factored as follows:

a^b + 1 = (a^(b/2) + 1) * (a^(b/2) - 1)

Applying this factoring to each term inside the brackets:

(0.2^2 + 1) = (0.2^(2/2) + 1) * (0.2^(2/2) - 1) = (0.2 + 1) * (0.2 - 1) = 1 * (-0.8) = -0.8

(0.2^4 + 1) = (0.2^(4/2) + 1) * (0.2^(4/2) - 1) = (0.2^2 + 1) * (0.2^2 - 1) = (-0.8) * (-0.96) = 0.768

(0.2^8 + 1) = (0.2^(8/2) + 1) * (0.2^(8/2) - 1) = (0.2^4 + 1) * (0.2^4 - 1) = 0.768 * (-0.9376) = -0.720896

(0.2^16 + 1) = (0.2^(16/2) + 1) * (0.2^(16/2) - 1) = (0.2^8 + 1) * (0.2^8 - 1) = (-0.720896) * (-0.992188) = 0.714042666048

(0.2^32 + 1) = (0.2^(32/2) + 1) * (0.2^(32/2) - 1) = (0.2^16 + 1) * (0.2^16 - 1) = 0.714042666048 * (-0.9999990463256836) = -0.7140416614750664

Now, we have simplified each term inside the brackets, so we can put them back together:

0.96 * [(0.2^2 + 1) * (0.2^4 + 1) * (0.2^8 + 1) * (0.2^16 + 1) * (0.2^32 + 1)]

= 0.96 * [(-0.8) * 0.768 * (-0.720896) * 0.714042666048 * (-0.7140416614750664)]

= 0.96 * 0.2767856490052298

= 0.265703327843206

So, the simplified expression is approximately 0.2657.