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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 23, 2022
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Note     1/a^2  + 1/b^2 =      [a^2 + b^2 ] / [ ab ] ^2

 

The sum of the roots =   11/5  =  a + b

 

Square both sides

 

121/25 =  a^2 + 2ab + b^2

 

The product of the roots =    4/5 = ab     so.....2ab =  8/5        and [ab]^2 = 16/25

 

So 

 

121/25 = a^2 + 2(4/5) + b^2

 

121/25 = a^2 + 8/5 + b^2

 

121/25  - 8/5 = a^2 + b^2

 

121/25 - 8/5 = a^2 + b^2

 

121/25 - 40/25 = a^2 + b^2

 

81/25 =  a^2 + b^2

 

So

 

1/a^2  + 1/b^2 =   [ 81/25] / [ 16/25 ] =    81 / 16

 

 

 

cool cool cool

 Jun 23, 2022

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