Question

2x+17x+32x+47x+...+227x+242x=4148​

Answer 1

Значит надо разложить выражение на множители

98х+54934х^2= 2х(49+27467х)

Answer 2

To solve the equation 2x + 17x + 32x + 47x + ... + 227x + 242x = 4148, we can use the formula for the sum of an arithmetic series.

The given equation can be rewritten as:

2x + 17x + 32x + 47x + ... + 227x + 242x = 4148

We can observe that the terms in the equation form an arithmetic series with the common difference of 15x. The first term is 2x, and the last term is 242x.

The formula for the sum of an arithmetic series is:

Sn = (n/2) * (a1 + an)

Where: Sn is the sum of the series. n is the number of terms in the series. a1 is the first term. an is the last term.

Using this formula, we can find the number of terms in the series:

242x = 2x + (n - 1) * 15x

Simplifying the equation:

242x = 2x + 15nx - 15x 242x - 2x + 15x = 15nx 225x = 15nx 15x(15 - n) = 0

Since x cannot be zero, we have:

15 - n = 0 n = 15

Therefore, the number of terms in the series is 15.

Now, we can substitute the values into the formula to find the sum:

Sn = (n/2) * (a1 + an) S15 = (15/2) * (2x + 242x) S15 = 7.5 * (2x + 242x) S15 = 7.5 * 244x S15 = 1830x

Given that the sum S15 is equal to 4148, we can set up the equation:

1830x = 4148

Solving for x:

x = 4148 / 1830 x ≈ 2.267

Therefore, the approximate value of x is 2.267.