Simple Problem

Algebra Level 1

100 1 2 − 99 9 2 10 1 2 − 9 9 2 \frac{1001^{2} - 999^{2}}{101^{2} - 99^{2}}


The answer is 10.

Josua Mustiko by Josua Mustiko , 23, Indonesia

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1 solution

Nelvson Shine
Jul 19, 2014

Since a 2 − b 2 a^2 - b^2 = ( a + b ) ( a − b ) (a+b)(a-b) ,

we can rewrite the problem to this :

100 1 2 − 99 9 2 10 1 2 − 9 9 2 \frac{1001^2 - 999^2}{101^2-99^2} = ( 1001 + 999 ) ( 10001 − 999 ) ( 101 + 99 ) ( 101 − 99 ) \frac{(1001+999)(10001-999)}{(101+99)(101-99)}

= 2000 × 2 200 × 2 \frac{2000 \times 2}{200 \times 2}

= 10 10

Then the answer shall be 10 10

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Are you going to be a constant problem writer in here, adit ? :P

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