Four operations

Algebra Level 1

Find the value of the following expression.

( 2019 + 2019 ) + ( 2019 2019 ) + ( 2019 × 2019 ) + ( 2019 ÷ 2019 ) \sqrt{(2019+2019)+(2019-2019)+(2019\times2019)+(2019\div 2019)}


The answer is 2020.

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3 solutions

Julian Yu
Apr 5, 2019

The expression is equal to 201 9 2 + 2 2019 + 1 = ( 2019 + 1 ) 2 = 2020. \sqrt{2019^2+2\cdot 2019+1}=\sqrt{(2019+1)^2}=2020.

FullSimplify [ ( n n ) + n n + n n + ( n + n ) ] ( n + 1 ) 2 ± n + 1 \text{FullSimplify}\left[\sqrt{(n-n)+n\,n+\frac{n}{n}+(n+n)}\right]\Rightarrow \sqrt{(n+1)^2}\Rightarrow \pm\left|\left|{n+1}\right|\right|

± 2020 \pm 2020

Eeshan Zele
Apr 20, 2019

Take n as 2019, and then simplify. That will become:

( n + n ) + ( n n ) + ( n × n ) + ( n / n ) = ( 2 n ) ( n 2 ) f a c t o r i z e = ( 1 + n ) 2 = ± n + 1 = ± 2020 \sqrt { (n+n)+(n-n)+(n\times n)+(n/n) } =\sqrt { (2n)(n^{ 2 }) } factorize =\sqrt { (1+n)^{ 2 } } =\pm n+1 =\boxed{\pm 2020}

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