Express x1^3+x2^3 in terms of the coefficients of the equation

     

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"Which is the value of the sum x1^3 + x2^3 if x1,x2 are solutions of the equation x^2-5x+6=0" giaynamdavinci.com Editorial, 7 Aug. 2010, https://www.giaynamdavinci.com/homework-help/which-value-sum-x1-3-x2-3-x1-x2-solutions-equation-188641.Accessed 23 Dec. 2022.

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f(x) = x^2 - 5x + 6

x1 & x2 are solution

We need to lớn determine the value of x1^3 + x2^3

From viete"s rule, we know that:

x1+ x2 = -b/a = 5.........(1)

x1*x2 = c/a = 6...........(2)

But f(x1) = f(x2) =0

Multiply 3 by x1 & (4) by x2

Add both equations:

= 5<(x1+x2)^2 - 2x1*x2> - 6(x1+x2)

= 5(5^2) - 5(2*6) - 6(5)

= 125 - 60 - 30

=125 - 90 = 35


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