设实数a、b满足a^2-8a+6=0及6b^2-8b+1=0,求ab+1/ab的值

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设实数a、b满足a^2-8a+6=0及6b^2-8b+1=0,求ab+1/ab的值

设实数a、b满足a^2-8a+6=0及6b^2-8b+1=0,求ab+1/ab的值
设实数a、b满足a^2-8a+6=0及6b^2-8b+1=0,求ab+1/ab的值

设实数a、b满足a^2-8a+6=0及6b^2-8b+1=0,求ab+1/ab的值
a²-8a+6=0 (1)
6b²-8b+1=0 ,两边同除以b²,得 (1/b)²-8(1/b)+6=0.(2)
由(1),(2)知:a和1/b 是x²-8x+6=0的两个根
则,
a/b=6 (3)
a+1/b=8 (4)
(4)÷(3),得 b+1/a=4/3 (5)
(4)×(5),得 ab+1/ab+2=32/3
则,ab+1/ab=26/3