Which is larger?

Algebra Level 2

Which is larger; x=(2014)(2013)(2012)(2011)(2010) or y=2012^{5}

2012^{5} (2014)(2013)(2012)(2011)(2009) (2014)(2013)(2012)(2011)(2010) (2014)(2013)(2012)(2011)(2010)=2012^{5}

Darven Diluculum by Darven Diluculum , 23, Philippines

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3 solutions

Uahbid Dey
Apr 1, 2015

5 Helpful 0 Interesting 0 Brilliant 0 Confused
Darven Diluculum
Jul 22, 2014

Express (2014)(2013)(2012)(2011)(2010) in terms of 2012.

(2012+2)(2012+1)(2012)(2012-1)(2012-2)

Use the special product,sum and difference of 2 squares

(2012+2)(2012-2)(2012+1)(2012-1)(2012) (2012^{2}-4)(2012^{2}-1)(2012) [(2012^{4})-5(2012^{2})+4][(2012)]

[(2012^{5})-5(2012^{3})+4(2012)]

From here you can determine what is larger

2 Helpful 0 Interesting 0 Brilliant 0 Confused

take a=12.

Now, we are comparing (a+2)(a+1)(a)(a-1)(a-2) and a^5

After opening LHS, we get (a^5)-5(a^2)+4a = a^5 + {4a-5(a^2)]

By putting a=12, you get to know [4a-5(a^2)] is a negative number.

Hence, it means in LHS, we are subtracting a (positive number) from a^5. Hence, RHS is greater than LHS.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

why taken a=12? i think it should be a=2012 isn't it?

Mohammed owais Khokhar - 6 years ago

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