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Let a and b be the solutions to 5x^2 - 11x + 4 = 0.  FInd 1/a^2 + 1/b^2.

 Jun 19, 2021
 #1
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1/a^2 + 1/b^2 = 13/7.

 Jun 19, 2021
 #2
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Try to write $1/a^2+1/b^2$ as an expression involving only $a+b$ and $ab$.  The values of $a+b$ and $ab$ can be obtained from the coefficients of $5x^2-11x+4$ almost by inspection. (Vieta)

 Jun 20, 2021

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