resolve into factor
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Given that, a/b + b/a = 1
Taking LCM of a and b, which is equal to ab.
a/b + b/a = (a² + b²)/ab = 1
or a² + b² = ab
Now,
a³+ b³ = ( a + b ) ( a² - ab - b² )
[ab = a² + b²]
=> a³+ b³ = ( a + b ) [ a² - (a² + b²) - b² ]
= ( a + b ) ( a² - a² - b² - b² )
= ( a + b ) ( -2 b² )
Therefore, a³+ b³ = ( a + b ) ( -2 b² )
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