SOLUTION: if a,b are the roots of the equation 2x2+6x-10=0.Find a4+b4,a3-b3,a6+b6,a6-b6

Since a, b are roots of 



they are also roots of the monic polynomial equation found
by dividing through by 2



The sum of the roots is the negartive of the coefficient of x,
-3.  The product of the roots is the constant number or -5
The absolute value of the difference of the roots is 


If we let a be the larger root, then   

So , , 

So 

So 

So 

Square both sides:









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But also 

So  or 




But also ,

So  or



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Edwin