Advertisement Remove all ads

Evaluate: 483 − 303 − 183 - Mathematics

Answer in Brief

Evaluate:

483 − 303 − 183

Advertisement Remove all ads

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.

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Exercise 4.5 | Q 2.2 | Page 29
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×