Question

I ASK SO MUCH OF YOUR HELP, PLEASE. Let x + y = 11 and x^2 + y^2 = 325. What is the value of x^3 + y^3? PLEASE EXPLAIN, TOO .

Answer 1

Answer: 4697

Step-by-step explanation:

x + y = 11 ......... i

x² + y² = 325 ........ ii

From equation i

x + y = 11

Therefore, x = 11 - y....... iii

Put equation iii into equation ii

x² + y² = 325

(11 - y)² + y² = 325

(11 - y)(11 - y) + y² = 325

121 - 11y - 11y + y² + y² = 325

121 - 22y + 2y² = 325

121 - 325 - 22y + 2y² = 0

2y² - 22y -204 = 0

2y² - 34y + 12y - 204 = 0

2y(y - 17) + 12(y - 17) = 0

(y - 17) = 0

y = 0 + 17

y = 17

Since x + y = 11

x + 17 = 11

x = 11 - 17

x = -6

Therefore, x³ + y³

= (-6)³ + (17)³

= -216 + 4913

= 4697