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Question

Miscellaneous Problem.
Calculate x41,+x42 where x1andx2 are the roots of the equation 3x2 - 5x + 1 = 0.

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Solution

3x25x+1=0(ax2+bx+c=0)
Let roots be x1 & x2
Sum of roots i.e. x1+x2=ba=(5)3=53
Products of roots i.e. x1x2=ca=13
Now, (x21+x22)=(x1+x2)22x1x2
=(5/3)22(1/3)=19/9
x41+x42=(x21+x22)22x21x22
=(19/9)22(1/3)2=343/81

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