Question

芽瑠

この問題教えてください

6. a, b を定数とする. xについての3つの2次方程式
x2+(1-a)x-a=0,
2x2-(8+b)x+46=0,
3x2-(a+66)x+2ab=0,
には,正の共通の解が一つある.このとき, a=□,
b=□である.
(23 大阪経済大)

Answer 1

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Dw

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芽瑠

a/3とb/2はなぜ除外しているのですか？

Dw

Each equation has a solution that is correct.
Therefore,
1. x is either equal to a or -1
2. x is either equal to b/2 or 4
3. x is either equal to a/3 or 2b

The problem also states that x is positive,
so we have reason to conclude that x ≠ -1,
which means x = a
Since x = a , x cannot be equal to a/3
which means x = 2b
Since x = 2b , x cannot be equal to b/2
which means x = 4

Therefore, we have:
1. x = a
3. x = 2b
2. x = 4

Dw

Sry for my bad Japanese. If there's anything you don't understand, just feel free to ask👌

芽瑠

Thank you so much !
I could understand