If a/b+b/a=-1, find a 3 -b 3 .
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If a/b + b/a = -1, then
taking LCM, and expanding, we get
(a^2 + b^2)/ab = -1
Or a^2 + b^2 = -ab
or a^2 + ab + b^2 = 0.
But we know
a^3 - b^3 = (a - b) (a^2 + ab + b^2)
From the above expression, it is clear that a^2 + ab + b^2 = 0.
Therefore, a^3 - b^3 = (a - b) * 0 = 0.
taking LCM, and expanding, we get
(a^2 + b^2)/ab = -1
Or a^2 + b^2 = -ab
or a^2 + ab + b^2 = 0.
But we know
a^3 - b^3 = (a - b) (a^2 + ab + b^2)
From the above expression, it is clear that a^2 + ab + b^2 = 0.
Therefore, a^3 - b^3 = (a - b) * 0 = 0.
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