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Question
Write the value of 303 + 203 − 503.
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Solution
The given expression is
303 + 203 − 503.
Let a=30,b= 20 and c = - 50. Then the given expression becomes
`30^3 + 20^3 - 50^3 = a^3 +b^3 + c^3`
Note that
`a+b+c = 30 + 20 + (-50)`
` =30 + 20 - 50`
` =0`
Recall the formula
`a^3 + b^3 +c^3 - 3abc = (a+b+c)(a^2 +b^2 + c^2 - ab - bc - ca)`
When a + b + c = 0, this becomes
`a^3 +b^3 + c^3 - 3abc = 0.(a^2 + b^2 +c^2 - ab - bc - ca)`
`a^3 +b^3+c^3 = 3abc`
So, we have the new formula
`a^3 +b^3+c^3 = 3abc` , when a + b + c = 0,.
Using the above formula, the value of the given expression is
`a^3 +b^3+c^3 = 3abc`
`30^3 + 20^3 - 50^3 = 3.(30).(20).( -50)`
`30^3 + 20^3 - 50^3 = -90000`
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