Answer:
The numbers are 3 , 4 , 5
Explanation:
- Consecutive numbers are the number after each other like 1 , 2 , 3, .....
- We have three consecutive numbers
- Assume that the smallest is x, the middle is x + 1 and the largest
is x + 2
- The fourth power means power 4
- The fourth power of the smallest means

- Eight times the middle number means 8(x + 1)
- The sum of the fourth power of the smallest integer and eight
times the middle integer means

∴ The sum of the fourth power of the smallest integer and eight
times the middle integer =
⇒ (1)
- Two times the square of the largest integer means 2(x + 2)²
- Increased by 63 ⇒ means add 63
∴ Two times the square of the largest integer increased by 63 =
2(x + 2)² + 63 ⇒ (2)
- The sum of the fourth power of the smallest integer and eight times
the middle integer is equal to two times the square of the
largest integer increased by 63
∵ is equal means =
- Equate (1) and (2)
∴
= 2(x + 2)² + 63
- Lets simplify it
∵

∴

- Subtract 8 and 8x from both sides
∴

- Subtract 2x² and 63 from both sides
∴

- Now use your calculator to find the value of x
- The values of x are -3 , 3 , i√7 , -i√7
∵ The numbers are positive integers
∴ The value of x is 3
∴ The numbers are 3 , 4 , 5