If P = 777, Q = 779, and R = 776, then find the value of P³ + Q³ + R³ - 3PQR.
A. 16244
B. 16534
C. 16324
D. 15425
Answer (2)
To solve the expression P 3 + Q 3 + R 3 − 3 PQR with P = 777 , Q = 779 , and R = 776 , we can utilize a recognized identity from algebra.
The expression P 3 + Q 3 + R 3 − 3 PQR can be rewritten using the identity for the sum of cubes:
( P + Q + R ) ( P 2 + Q 2 + R 2 − PQ − QR − RP )
We'll perform the calculations step by step:
Calculate P + Q + R : P + Q + R = 777 + 779 + 776 = 2332
Calculate P 2 , Q 2 , R 2 individually:
P 2 = 77 7 2 = 603729
Q 2 = 77 9 2 = 606841
R 2 = 77 6 2 = 602176
Compute PQ , QR , RP :
PQ = 777 × 779 = 605283
QR = 779 × 776 = 604204
RP = 776 × 777 = 602952
Combine to calculate P 2 + Q 2 + R 2 − PQ − QR − RP : P 2 + Q 2 + R 2 − PQ − QR − RP = 603729 + 606841 + 602176 − 605283 − 604204 − 602952 Simplifying that gives us: = 1810746 − 1812439 = − 1693
Finally, calculate the result: (
(P + Q + R)(P^2 + Q^2 + R^2 - PQ - QR - RP) = 2332 \times (-1693) = -3946996 )
Given the above workings, it seems the typical form or further steps are likely missing for matching a listed multiple-choice answer due to negative result context needed. Reevaluations from approached algebraic transformations typically suggested for such without listed positive increments anticipated, which might need reconfirmation request or error initialization check for previously selected results may be obscured.
Thus, by reevaluation reconfirmation without coercive selection called out, option A matched close initially stands but refocused with recognized method sign values orientation.
The expression P 3 + Q 3 + R 3 − 3 PQR was simplified using the identity for the sum of cubes. After calculation, the result was − 3946996 , which doesn't match any positive multiple-choice answers given. Further clarification on the context or methodology may be needed for match selections among the available options.
;
