http://store1.up-00.com/Mar12/3Zb90292.jpg is equal square number ,what is the number?

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- Apr 8th 2012, 05:05 AMMhmh96Square number
http://store1.up-00.com/Mar12/3Zb90292.jpg is equal square number ,what is the number?

- Apr 8th 2012, 05:24 AMSylvia104Re: Square number
Let $\displaystyle n=123456.$ Then the expression is $\displaystyle (n+1)+n+n^2=1+2n+n^2.$ Now factorize $\displaystyle 1+2n+n^2.$ (Smile)

- Apr 8th 2012, 05:39 AMMhmh96Re: Square number
(n+1)(n+1)?

- Apr 8th 2012, 07:14 AMSorobanRe: Square number
Hello, Mhmh96

You may have missed the point of Sylvia's hint . . .

Quote:

$\displaystyle 123457 \;+\; 123456 \;+\; (123456)^2\text{ is the square of an integer.}\;\text{ What is the integer?}$

Look at what we have:

$\displaystyle (123456)^2 + 123456 + 123457$

. . $\displaystyle =\;(123456)^2 + 123456 + 123456 + 1$

. . $\displaystyle =\;(123456)^2 + 2(123456) + 1$

. . $\displaystyle =\;(123456 + 1)^2$

. . $\displaystyle =\;(123457)^2$

$\displaystyle \text{Answer: }\:123457$

- Apr 9th 2012, 07:46 AMMhmh96Re: Square number
thanks for your help,and for correcting the question.

- Apr 9th 2012, 07:54 AMMhmh96Re: Square number
Now i understand what is the hint