Write as whole square

**razemsoft21** · October 6th 2010, 12:15 PM

Can you please write equation
$n(n+1)(n+2)(n+3)+1$
as whole square

like writing ${x}^2+4x+4=(x+2)(x+2) = {(x+2)}^{2}$

My Try:
$n(n+1)(n+2)(n+3)+1={n}^{4}+{6n}^{3}+{11n}^{2}+6n+1$
and this equation has 2 pairs of equal roots, and they are not integers

**mr fantastic** · October 6th 2010, 12:17 PM

Originally Posted by razemsoft21

Can you please write equation
$n(n+1)(n+2)(n+3)+1$
as whole square

like writing ${x}^2+4x+4=(x+2)(x+2) = {(x+2)}^{2}$

My Try:
$n(n+1)(n+2)(n+3)+1={n}^{4}+{6n}^{3}+{11n}^{2}+6n+1$
and this equation has 2 pairs of equal roots, and they are not integers

factorise x(x+1)(x+2)(x+3&#4 1; + 1 - Wolfram|Alpha

**razemsoft21** · October 6th 2010, 04:34 PM

Originally Posted by mr fantastic

factorise x(x+1)(x+2)(x+3&#4 1; + 1 - Wolfram|Alpha

Correct answer thank you.
can you please show me the way you solve it ?

**mr fantastic** · October 6th 2010, 06:26 PM

Originally Posted by razemsoft21

Correct answer thank you.
can you please show me the way you solve it ?

Can you reverse engineer a solution from the answer ...? See how you go.

**Soroban** · October 6th 2010, 07:39 PM

Hello, razemsoft21!

Write as a square: . $n(n+1)(n+2)(n+3)+1$

We have: . $\bigg[n(n+3)\bigg]\,\bigg[(n+1)(n+2)\bigg] + 1$

. . $=\;\bigg[n^2 + 3n\bigg]\,\bigg[n^2+3n + 2\bigg] +1$

. . $=\; \bigg[n^2 + 3n +1 - 1\bigg]\,\bigg[n^2 + 3n + 1 + 1\bigg] + 1$

. . $=\; \bigg[(n^2 + 3n +1) - 1\bigg]\,\bigg[(n^2 + 3n + 1) + 1\bigg] + 1$

. . $=\;\bigg[(n^2+3n + 1)^2 - 1^2\bigg] + 1$

. . $=\;(n^2 + 3n + 1)^2$

Thread: Write as whole square

LinkBack

Thread Tools

Display

Write as whole square

Similar Math Help Forum Discussions

Find distance between a point on one side of a square, and a corner of the square.

a.complete the square to write the quadratic equation f(x)-3x^2+6x+5 in standard form

complete the square to write the quadratic equation f(x)-3x^2+6x+5 in standard form

Prove that the square root of a non-square number is irrational

Write an Equation? I dont know how to write an equation..

Search Tags