Question

(1-4x) (1+4x+16x^2)+x^2(64x-25)=0

Answer 1

a³ - b³ = (a - b)(a² + ab + b²)

(1-4x) (1+4x+16x^2)+x^2(64x-25)=0

1³-(4x)³ +64x^3-25x^2=0

1 - 64x^3 + 64x^3 - 25x^2 = 0

25x^2 = 1

x^2 = 1/25

|x| = 1/5

x = ± 1/5

Answer 2

To solve the equation (1 - 4x)(1 + 4x + 16x^2) + x^2(64x - 25) = 0, you can follow these steps:

1. Expand the expressions on both sides of the equation:

   (1 - 4x)(1 + 4x + 16x^2) + x^2(64x - 25) = 0

   Expand the first term using the distributive property:

   (1 + 4x + 16x^2 - 4x - 16x^2 - 64x^3) + x^2(64x - 25) = 0

2. Simplify and collect like terms:

   1 + (4x - 4x) + (16x^2 - 16x^2) - 64x^3 + 64x^3 - 25x^2 = 0

   The terms (4x - 4x) and (16x^2 - 16x^2) both cancel out:

   1 - 25x^2 = 0

3. Rearrange the equation:

   1 = 25x^2

4. Solve for x by taking the square root of both sides:

   √(1) = √(25x^2)

   1 = 5x

5. Finally, solve for x:

   x = 1/5

So, the solution to the equation (1 - 4x)(1 + 4x + 16x^2) + x^2(64x - 25) = 0 is x = 1/5.