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Question

If α2=5α3,β2=5β3 then the value of αβ+βα

A
19/3
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B
25/3
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C
19/3
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D
none of these
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Solution

The correct option is A 19/3
α2=5α3 and β2=5β3
α25α+3=0 and β25β+3=0
α=5±25122 and β=5±25122

α=5±132 and β=5±132
Since, αβ
So, take α=5+132 and β=5132
Now, αβ=5+1325132=5+13513=(5+13)2(5)2(13)2

=25+13+10132513

=38+101312

=19+5136 ---- ( 1 )

Now, βα=51325+132=5135+13=(513)2(5)2(13)2

=25+1310132513

=38101312

=195136 ----- ( 2 )

αβ+βα=19+5136+195136 [ From ( 1 ) and ( 2 ) ]


αβ+βα=386=193

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