Question

(61^ 3 + 49 ^ 3)/110 + 61 * 49

Answer 1

a³ + b³ =(a + b)(a² - ab + b²)

(a - b)² = a² - 2ab + b²

(a + b)² = a² + 2ab + b²

61 = 60 + 1

49 = 50 - 1

используя эти формулы этот пример можно решить "в уме"

(61^ 3 + 49 ^ 3)/110 + 61 * 49 = (61 + 49)(61² - 61*49 + 49²)/110 + 61*49 = 110(61² - 61*49 + 49²)/110 + 61*49 = 61² - 61*49 + 49² + 61*49 = 61² + 49² = (60 + 1)²  + (50 - 1)² = 60² + 2*60 + 1 + 50² - 2*50 + 1 = 3600 + 2500 + 20 + 2 = 6122

Answer 2

(61^ 3 + 49 ^ 3)/110 + 61 * 49 = (226981 + 117649) / 110 + 2989 = 344630 / 110 + 2989 = 3133 + 2989 = 6122

Answer 3

Let's break down the expression step by step:

1. Calculate the cubes of 61 and 49:

   • 61^3 = 226,981
   • 49^3 = 117,649

2. Add the cubes of 61 and 49:

   • 226,981 + 117,649 = 344,630

3. Divide the result from step 2 by 110:

   • 344,630 / 110 = 3,142

4. Multiply 61 by 49:

   • 61 * 49 = 2,989

Now, add the result from step 3 to the result from step 4:

• 3,142 + 2,989 = 6,131

So, (61^3 + 49^3)/110 + 61 * 49 = 6,131.