+0  
 
0
83
2
avatar

If ab = 15 and a^2 + b^2 = 40, then find (a + b)^4 - (a - b)^4.

 Jan 10, 2020
 #1
avatar+109739 
+1

ab  =15     a^2 + b^2  =40

 

Note  that    (a + b)^4  - ( a - b)^4 =   [ (a + b)^2  + ( a - b)^2  ]  [ (a + b)^2 - (a - b)^2]  =

 

[ a^2 + 2ab + b^2  + (a^2  - 2ab + b^2 ]   [  ( a^2 + 2ab + b^2)  - (a^2 - 2ab + b^2 ]  =

 

[ 2a^2 + 2b^2  ]   [ 4ab ]  =

 

2 [ a^2 + b^2 ] * 4 [ ab ] =

 

2 [40 ] * 4 [15]  =

 

80  *  60  =

 

4800   

 

 

 

cool cool cool

 Jan 10, 2020
 #2
avatar+24422 
+2

If ab = 15 and a^2 + b^2 = 40, then find (a + b)^4 - (a - b)^4.

 

\(\begin{array}{|rcll|} \hline (a+b)^2 &=& a^2+b^2+2ab \\ &=& 40+2*15 \\ &=& 70 \\ \mathbf{(a+b)^4} &=& \mathbf{70^2} \\\\ (a-b)^2 &=& a^2+b^2-2ab \\ &=& 40-2*15 \\ &=& 10 \\ \mathbf{(a-b)^4} &=& \mathbf{10^2} \\ \\ (a+b)^4 - (a-b)^4 &=& 70^2-10^2 \\ \mathbf{ (a+b)^4 - (a-b)^4 } &=& \mathbf{4800} \\ \hline \end{array}\)

 

laugh

 Jan 10, 2020

31 Online Users

avatar
avatar