Question

(4x+1)^(3)=16x^(2)(4x+3)+2(5x+4)

Answer 1

(4x+1)³=16x²(4x+3)+2(5x+4)

(a + b)³ = a³ + 3a²b + 3ab² + b³

64x³ + 48x² + 12x + 1 = 64x³ + 48x² + 10x + 8

2x = 7

x = 7/2

Answer 2

(4х+1)³=16х²(4х+3)+2(5х+4)

64х³+3*16х²*1+3*4х*1+1=64х³+48х²+10х+8

64х³+48х²+12х+1=64х³+48х²+10х+8

64х³-64х³+48х²-48х²+12х-10х+1-8=0

2х-7=0

2х=7

х=7:2

х=3,5

На всякий пожарный, проверьте самостоятельно. Вдруг я тоже ошибку допустил.

Answer 3

Let's solve the equation step by step. The equation you provided is:

(4x + 1)^3 = 16x^2(4x + 3) + 2(5x + 4)

To solve for x, we'll first expand the left-hand side (LHS) using the binomial formula, and then simplify the right-hand side (RHS):

Step 1: Expand the left-hand side (LHS):

(4x + 1)^3 = (4x + 1)(4x + 1)(4x + 1) = (16x^2 + 8x + 1)(4x + 1) = 16x^3 + 8x^2 + 4x + 16x^2 + 8x + 1 = 16x^3 + 24x^2 + 12x + 1

Step 2: Simplify the right-hand side (RHS):

16x^2(4x + 3) + 2(5x + 4) = 64x^3 + 48x^2 + 10x + 8

Now the equation becomes:

16x^3 + 24x^2 + 12x + 1 = 64x^3 + 48x^2 + 10x + 8

Step 3: Move all terms to one side of the equation to set it to zero:

16x^3 + 24x^2 + 12x + 1 - 64x^3 - 48x^2 - 10x - 8 = 0

Step 4: Combine like terms:

-48x^3 - 24x^2 + 2x - 7 = 0

The equation is now in standard form (ax^3 + bx^2 + cx + d = 0). Now, we'll try to solve for x. Unfortunately, this is a cubic equation, which does not have a simple algebraic solution like quadratic equations.

One way to proceed is to use numerical methods or calculators to find approximate solutions. For example, you can use numerical root-finding methods like the Newton-Raphson method or graphing calculators to find the values of x that satisfy the equation. Another option is to use software like Wolfram Alpha or MATLAB to find the approximate solutions.

However, without specific constraints or further instructions, we cannot find exact solutions to this equation using simple algebraic methods.