Question

Решите. 4x^3 - 8x^2 + 2x + 3 при x= 0.5*(1+√3)

Answer 1

Ответ:

1

Объяснение:

4(0.5(1+√3))^3-8(0.5(1+√3))^2+2(0.5(1+√3))+3=2^2*0.5^3*(1+√3)^3-2^3*0.5^2*(1+√3)^2+2(0.5+0.5√3)+3=...

Answer 2

To solve the expression 4x^3 - 8x^2 + 2x + 3 for a specific value of x, which is x = 0.5*(1 + √3), we simply substitute this value into the expression and calculate the result.

Step 1: Substitute x = 0.5*(1 + √3) into the expression:

4*(0.5*(1 + √3))^3 - 8*(0.5*(1 + √3))^2 + 2*(0.5*(1 + √3)) + 3

Step 2: Perform the calculations:

Let's first simplify the terms:

0.5*(1 + √3) = 0.5 + 0.5√3

Now, substitute this value into the expression:

4*(0.5 + 0.5√3)^3 - 8*(0.5 + 0.5√3)^2 + 2*(0.5 + 0.5√3) + 3

Step 3: Calculate each part of the expression:

a) (0.5 + 0.5√3)^3: (0.5 + 0.5√3)^3 = (0.5)^3 + 3*(0.5)^2*(0.5√3) + 3*(0.5)*(0.5√3)^2 + (0.5√3)^3 (0.5 + 0.5√3)^3 = 0.125 + 0.375√3 + 0.375√3 + 0.375√3 + 0.375√3√3 + 0.125√3√3 + 0.125√3√3 + 0.375√3√3 (0.5 + 0.5√3)^3 = 0.125 + 0.75√3 + 0.375(√3)^2 + 0.5(√3)^3 (0.5 + 0.5√3)^3 = 0.125 + 0.75√3 + 0.375(3) + 0.5(3√3) (0.5 + 0.5√3)^3 = 0.125 + 0.75√3 + 1.125 + 1.5√3 (0.5 + 0.5√3)^3 = 1.25 + 2.25√3

b) (0.5 + 0.5√3)^2: (0.5 + 0.5√3)^2 = (0.5)^2 + 2*(0.5)*(0.5√3) + (0.5√3)^2 (0.5 + 0.5√3)^2 = 0.25 + 0.5√3 + 0.25(√3)^2 (0.5 + 0.5√3)^2 = 0.25 + 0.5√3 + 0.25(3) (0.5 + 0.5√3)^2 = 0.25 + 0.5√3 + 0.75 (0.5 + 0.5√3)^2 = 1 + 0.5√3

c) 2*(0.5 + 0.5√3): 2*(0.5 + 0.5√3) = 20.5 + 20.5√3 2*(0.5 + 0.5√3) = 1 + √3

Now, substitute these values back into the original expression:

4*(1.25 + 2.25√3) - 8*(1 + 0.5√3) + (1 + √3) + 3

Step 4: Calculate the final result:

4*(1.25 + 2.25√3) = 5 + 9√3 8*(1 + 0.5√3) = 8 + 4√3

Now, put it all together:

(5 + 9√3) - (8 + 4√3) + (1 + √3) + 3

Combine like terms:

5 - 8 + 1 + 3 + (9√3 - 4√3 + √3)

Simplify the constants:

1 + 3 + 9√3 - 4√3 + √3

Combine like terms again:

4 + 6√3

So, the final result when x = 0.5*(1 + √3) is:

4x^3 - 8x^2 + 2x + 3 = 4 + 6√3