Let's compare each expression:
For the first expression:
2 to the power of 2 is equal to 4.
1 to the power of 2 is equal to 1.
2 + 1 is equal to 3.
For the second expression:
3 to the power of 2 is equal to 9.
2 to the power of 2 is equal to 4.
3 + 2 is equal to 5.
For the third expression:
4 to the power of 2 is equal to 16.
3 to the power of 2 is equal to 9.
4 + 3 is equal to 7.
Now, let's determine the pattern.
For the first expression, we have:
(2^2) - (1^2) = 4 - 1 = 3
For the second expression, we have:
(3^2) - (2^2) = 9 - 4 = 5
For the third expression, we have:
(4^2) - (3^2) = 16 - 9 = 7
The pattern appears to be the sum of the two numbers being raised to the power of 2, subtracted from their individual squares.
Now let's evaluate the expression:
617 283 945 062 to the power of 2 - 617 283 945 061 to the power of 2
Using the pattern we observed, we have:
(617 283 945 062^2) - (617 283 945 061^2)
Calculating the squares, we get:
(381 072 399 571 497 256 490 272 244) - (381 072 399 571 497 256 490 272 121)
Subtracting the two numbers, we find:
123
Therefore, 617 283 945 062 to the power of 2 - 617 283 945 061 to the power of 2 is equal to 123.
Compare
2 to the power of 2 - 1 to the power of 2 and 2+1
3 to the power of 2 - 2 to the power of 2 and 3+2
4 to the power of 2 - 3 to the power of 2 and 4+3
find a pattern and use it to evaluate 617 283 945 062 to the power of 2 - 617 283 945 061 to the power of 2
1 answer
1 answer