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Solve          (t^2 - 82)^2 = 324
in real numbers.

 May 4, 2020
 #1
avatar+111326 
+1

(t^2 - 82)^2  =  324     expand

 

t^4  - 164t^2  + 6724  = 324    subtract 324 from borh sides

 

t^4 - 164t^2  +  6400   =   0     we can factor this as

 

( t^2  - 100) ( t^2 - 64)  =  0    factor these terms  as differences of squares

 

(t-10)(t+10)(t-8)(t+8)  =0

 

Setting each factor to 0  and solving for t  produces  the solutions

 

t  =10   t  = -10    t  =  8    t  = -8

 

cool cool cool

 May 4, 2020
 #2
avatar+87 
+1

Thanks!

 May 4, 2020
 #3
avatar+111326 
0

No prob  !!!!

 

 

cool cool cool

CPhill  May 4, 2020

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