Dividing a7+b7 by a+b, prove the formula
Answers
Given : a⁷ + b⁷
To find : Divide by a + b
Solution:
a⁶ + b⁶ -a⁵b - ab⁵ + a⁴b² + a²b⁴ - a³b³
(a + b) _| a⁷ + b⁷ |_
a⁷ + a⁶b
______________
b⁷ - a⁶b
b⁷ + ab⁶
_____________
-a⁶b - ab⁶
-a⁶b -a⁵b²
_________________
- ab⁶ + a⁵b²
-ab⁶ -a²b⁵
______________
a⁵b² + a²b⁵
a⁵b² + a⁴b³
______________
a²b⁵ - a⁴b³
a²b⁵ a³b⁴
_________________
-a⁴b³ - a³b⁴
-a⁴b³ - a³b⁴
__________
0
_____________
=> a⁷ + b⁷ = (a + b) ( a⁶ + b⁶ -a⁵b - ab⁵ + a⁴b² + a²b⁴ - a³b³)
a⁷ + b⁷ = (a + b) ( a⁶ -a⁵b + + a⁴b² - a³b³ + a²b⁴ - ab⁵ + b⁶)
(a⁷ + b⁷) /(a + b) = a⁶ -a⁵b + + a⁴b² - a³b³ + a²b⁴ - ab⁵ + b⁶
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Answer:
(a5+b6) = a4+a3b+a2b2+ab3+b4