Question

if a,b,c are positive integers such that a^2+2b^2-2ab=169 and 2bc -c^2 =169.then find (a+b+c)

Answer 1

Given :    a² + 2b²  - 2ab  = 169  , 2bc -c² =169  

To find : a + b + c

Solution:

a² + 2b²  - 2ab  = 169

2bc -c² =169  

Equating both

a² + 2b²  - 2ab  = 2bc -c²

=> a²  + b² - 2ab + b²  + c²  - 2bc = 0

=> (a - b)² + (b - c)² = 0

=> a - b = 0   & b - c = 0

=> a = b  & b = c

=> a = b = c

a² + 2b²  - 2ab  = 169

=> a² + 2a² - 2a² = 169

=> a² = 169

=> a = 13

a = b = c = 13

a + b + c = 13 + 13 + 13 = 39

a + b + c = 39

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Answer 2

Answer:

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