An algebra problem by Fermin Cabrieto

Algebra Level 1


The answer is 400.

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2 solutions

Fermin Cabrieto
Aug 9, 2015

(101+99)(101-99) =(200)(2) =400

Using the usual a 2 b 2 = ( a + b ) ( a b ) { a }^{ 2 }-{ b }^{ 2 }=\quad (a+b)\quad (a-b) = 101 2 99 2 = ( 101 99 ) x ( 101 + 99 ) = ( 2 ) x ( 200 ) = 400 ={ 101 }^{ 2 }\quad -\quad { 99 }^{ 2 }\\ =(101-99)\quad x\quad (101+99)\\ =(2)\quad x\quad (200)\\ =400

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