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Question
Evaluate:
483 − 303 − 183
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Solution
Given 483 − 303 − 183
We shall use the identity `a^3 + b^3 + c^3 - 3abc = (a+b+c) (a^2 +b^2 + c^2 - ab - bc+ ca)`
Let Take a= 48 , b = 30,c =-18
`a^3 + b^3 +c^3 - 3abc = (a+b+c)(a^2 +b^2 + c^2 - ab - ab - ca)`
`a^3 + b^3 +c^3 = (a+b+c)(a^2 +b^2 + c^2 - ab - ab - ca) + 3abc`
`a^3 + b^3 +c^3 - 3abc = (48+30+18)(a^2 +b^2 + c^2 - ab - ab - ca)+3abc`
`a^3 + b^3 +c^3 = 0 xx (a^2 +b^2 + c^2 - ab - ab - ca) + 3abc`
`a^3 + b^3 +c^3 = + 3abc`
`48^3 - 30^3 - 18^3 = 3xx 48 xx -30 xx -18`
= 77760
Hence the value of `25^3 - 75^3 + 50^3`is 77760.
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