Question

A common factor of (13^7+11^7) and (13^5+11^5)​

Answer 1

Answer:

13^5+11^5(13^2+11^2)

Answer 2

Given : $(13^7 + 11^5) ,(13^5 + 11^5)$

Step-by-step explanation:

we have given $(13^7 + 11^5) ,(13^5 + 11^5)$

for n = odd

we use the algebraic identities

$x^n +y^n = (x+y)(x^(^n^-^1^)- x^(^n^-^2^)y+x^(^n^-^3^)y^2+...x^2^y^(^n^-^3^)-xy^(^n^-^2^)+y^(^n^-^1^)$

thus

$13^7 + 11^7 \\\\(13+11)(13^6- 13^5 \times 11+13^4\times 11^213^3\times 11^3+13^2\times 11^4-13\times 11^5+11^6)$

and

$13^5 + 11^5 \\\\(13+11)(13^4- 13^3 \times 11+13^2\times 11^2- 13\times 11^3+11^4)$

thus ,

The common factor is  (13+11)  = 24

#Learn more :

https://brainly.in/question/9983572