We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
655
2
avatar

Hi can anyone help me?

How to solve 12345678^4-(12345679^2+1)(12345677^2+1)?

The answer is -4 but whyy?? Thanks so much!:)

 Aug 19, 2015

Best Answer 

 #1
avatar+22869 
+8

$$\small{\text{$
12345678^4-(12345679^2+1)(12345677^2+1)
$}}$$

 

$$\small{\text{
We set $x = 12345678 $, so we have $x^4 -[ (x+1)^2+1 ]\cdot
[ (x-1)^2 +1 ]
$}}$$

 

$$\small{\text{$
\begin{array}{lcl}
x^4 -[ (x+1)^2+1 ]\cdot [ (x-1)^2 +1 ] \\
&= & x^4 -[ x^2+2x+1+1 ]\cdot [ x^2-2x+1+1 ] \\
&= & x^4 -[ x^2+2x+2 ]\cdot [ x^2-2x+2 ] \\
&= & x^4 -[ (x^2+2)+2x ]\cdot [ (x^2+2)-2x ] \\
&= & x^4 -[ (x^2+2)^2 -(2x)^2 ] \\
&= & x^4 -[ x^4 +4x^2 + 4 -4x^2 ] \\
&= & x^4 -[ x^4 + 4 ] \\
&= & x^4 -x^4 - 4 \\
\mathbf{ x^4 -[ (x+1)^2+1 ]\cdot [ (x-1)^2 +1 ]}& \mathbf{= } & \mathbf{ - 4 } \\
\end{array}
$}}$$

 

 Aug 19, 2015
 #1
avatar+22869 
+8
Best Answer

$$\small{\text{$
12345678^4-(12345679^2+1)(12345677^2+1)
$}}$$

 

$$\small{\text{
We set $x = 12345678 $, so we have $x^4 -[ (x+1)^2+1 ]\cdot
[ (x-1)^2 +1 ]
$}}$$

 

$$\small{\text{$
\begin{array}{lcl}
x^4 -[ (x+1)^2+1 ]\cdot [ (x-1)^2 +1 ] \\
&= & x^4 -[ x^2+2x+1+1 ]\cdot [ x^2-2x+1+1 ] \\
&= & x^4 -[ x^2+2x+2 ]\cdot [ x^2-2x+2 ] \\
&= & x^4 -[ (x^2+2)+2x ]\cdot [ (x^2+2)-2x ] \\
&= & x^4 -[ (x^2+2)^2 -(2x)^2 ] \\
&= & x^4 -[ x^4 +4x^2 + 4 -4x^2 ] \\
&= & x^4 -[ x^4 + 4 ] \\
&= & x^4 -x^4 - 4 \\
\mathbf{ x^4 -[ (x+1)^2+1 ]\cdot [ (x-1)^2 +1 ]}& \mathbf{= } & \mathbf{ - 4 } \\
\end{array}
$}}$$

 

heureka Aug 19, 2015
 #2
avatar+102761 
0

That is cool Heureka  

 Aug 19, 2015

12 Online Users

avatar
avatar