Question
(5.53 – 4.07) 2/(4.07 – 3.15)(3.15 –
5.53) + (4.07 – 5.53) 2/(3.15 – 5.53)(5.53 – 4.07) + (3.15 – 5.53) 2/(5.53 – 4.07)(4.07 – 3.15) is simplified toSolution
According to the question, Let a = 5.53 – 4.07, b = 4.07 – 3.15 & c = 3.15 – 5.53 a + b + c = 0 Therefore, a3 + b3 + c3 = 3abc Dividing both sides by “abc”, we get (a3 + b3 + c3)/abc = 3abc/abc a2/bc + b2/ca + c2/ab = 3 Hence, (5.53 – 4.07)2/(4.07 – 3.15)(3.15 – 5.53) + (4.07 – 5.53)2/(3.15 – 5.53)(5.53 – 4.07) + (3.15 – 5.53)2/(5.53 – 4.07)(4.07 – 3.15) = 3
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