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Let a and b be the solutions to 5x^2 - 11x + 4 = 4x^2 + 12x - 13. Find 1/a^2 + 1/b^2.

 Feb 16, 2024
 #1
avatar+128732 
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Here : https://web2.0calc.com/questions/algebra_39593

 

 

cool cool cool

 Feb 16, 2024
 #2
avatar+394 
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Simplify, getting \({x}^{2}-23x+17=0\). We what to find \(\frac{1}{{a}^{2}}+\frac{1}{{b}^{2}}=\frac{{b}^{2}+{a}^{2}}{{(ab)}^{2}}\).

We see that what we want simplfies into \(\frac{(a+b)^2-2ab}{(ab)^2}\). By vieta's this is \(\frac{{23}^{2}-2*17}{{17}^{2}}=\frac{495}{289}\).

 Feb 16, 2024

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