What is a simple way to solve for the sum and difference of 2 cubes? for example, 27+64 and 64-1

(3 + 4x)(9 - 12x + 16x²) = 0

(4m - 1)(16m² + 4m + 1) = 0

Step-by-step explanation:

Here we have to solve the sum of two cubes which is

Now, the equation is

⇒ 3³ + (4x)³ = 0

⇒ (3 + 4x)[3² - 3(4x) + (4x)²] = 0

⇒ (3 + 4x)(9 - 12x + 16x²) = 0

So, (3 + 4x) = 0 or (9 - 12x + 16x²) = 0

Therefore, from the above two relation we can solve for x.

One root will be and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation.  

Again, we have to solve the difference of two cubes which is

Now, the equation is

⇒ (4m)³ - 1³ = 0

⇒ (4m - 1)[(4m)² + 4m(1) + 1²] = 0

⇒ (4m - 1)(16m² + 4m + 1) = 0

So, (4m - 1) = 0 or (16m² + 4m + 1) = 0

Therefore, from the above two relation we can solve for m.

One root will be and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation.  (Answer)

for the first question it would be the second answer for the second question it would be the third answer and for the third question it would be the first answer

step-by-step explanation:

step-by-step explanation: