+0  
 
0
70
2
avatar+96 

a^2 - b^2 = 8 and a*b = 2, find a^4 + b^4.

Olpers  Aug 25, 2018

Best Answer 

 #1
avatar+348 
+2

We have \({a}^{2} - {b}^{2} = 8\), which we can square both sides to get \(a^4 + b^4 - 2a^2b^2 = 8^2\). Since \(ab = 2\), we can square both sides again to get \(a^2b^2 = 2^2\). Then, we can subsitute that value into the equation; \(a^4 + b^4 - 2(4) = 8^2\) -> \(a^4 + b^4 - 8 = 64\) -> \(a^4 + b^4 = 72\).

 

- Daisy

dierdurst  Aug 25, 2018
 #1
avatar+348 
+2
Best Answer

We have \({a}^{2} - {b}^{2} = 8\), which we can square both sides to get \(a^4 + b^4 - 2a^2b^2 = 8^2\). Since \(ab = 2\), we can square both sides again to get \(a^2b^2 = 2^2\). Then, we can subsitute that value into the equation; \(a^4 + b^4 - 2(4) = 8^2\) -> \(a^4 + b^4 - 8 = 64\) -> \(a^4 + b^4 = 72\).

 

- Daisy

dierdurst  Aug 25, 2018
 #2
avatar+91027 
+2

a^2  - b^2   = 8   and  ab  = 2 

 

So 

 

(a^2 - b^2) (a^2 - b^2)  =  (8) * (8)

 

a^4  - 2(ab)^2 + b^4  = 64

 

a^4 + b^4  = 64 + 2(ab)^2

 

a^4 + b^4  =  64 + 2(2)^2

 

a^4 + b^4  = 64 + 8

 

a^4 + b^4  = 72

 

 

cool cool cool

CPhill  Aug 25, 2018

35 Online Users

avatar
avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.