Fractions and Squares

Algebra Level 2

12345678 9 2 12345679 0 2 + 12345678 8 2 − 12345678 9 2 − 2 \frac{123456789^{2}}{123456790^{2}+123456788^{2}-123456789^{2}-2}

Calculate the value of the expression above.


The answer is 1.0.

Wayne Alecxis Traya by Wayne Alecxis Traya , 22, Philippines

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2 solutions

Caeo Tan
Jun 12, 2015

let a=123456789

rewriting:

(a^2) / [(a+1)^2+(a-1)^2-a^2-2]

Expanding the binomials

(a^2)/[a^2+2a+1+a^2-2a+1-a^2-2]

Now, simplifying

(a^2)/(a^2)

Then simplifying again, we get 1, so the answer is "1"

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Chandan Mahapatra
Aug 10, 2014

Let 123456789=a, then the expression can be written as a^2/[(a+1)^2 +(a-1)^2 - 2]

Now the denominator is 2(a^2+1^2) - 2= 2a^2

so the answer is 1/2 and not 1 as given.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

I too got the same result.

Niranjan Khanderia - 6 years, 10 months ago

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Thanks. I have updated the answer to 0.5.

Calvin Lin Staff - 6 years, 10 months ago

Let 123456789=a, then the expression can be written as a^2/[(a+1)^2 +(a-1)^2 - a^2-2] Therefore denominator is a^2 and answer is 1

Khurram Sami - 6 years, 6 months ago

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Thanks. The problem phrasing was changed so that the answer is now 1. I have updated the answer accordingly.

In future, if you spot any errors with a problem, you can “report” it by selecting the “dot dot dot” menu in the lower right corner. You will get a more timely response that way.

Calvin Lin Staff - 6 years, 5 months ago

ummm why do i still end up with 1?

Martin Feussner - 6 years, 10 months ago

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