Given that a,b,x and y are real numbers such that

a+b=23
ax+by=79
ax²+by²=217
ax³+by³=691

Determine ax⁴+by⁴

(In reply to possible solution by broll)

Nice solution.

I got close but then I cheated.
I didn't try simplifying the 'heroic' equation.
Instead I subbed a and b into III and solved for y in terms of x using the quadratic equation.  (Gives two solutions with ±)
Then I subbed a,b, and y in for x and graphed IV on my calculator.
The + gives {x,y,b,a} = {-2,3,25,-2}
The - gives {x,y,b,a} = {3,-2,-2,25}

Is there a way to solve this without finding the values of all the variables?

Posted by Jer on 2013-10-07 09:59:24