find x for all real solution

👨🏻‍🏫 學術台數學

Jessie

2010-12-05 12:36 am

(1/x)+(1/a)=a+x
find x for all real solution.

please explain your answer with steps. Thankyou!

更新1:

RE: myisland8132 how to get the solution -a from x-(1/x)=(1/a)-a?

回答 (3)

[匿名]

2010-12-12 6:45 am

✔ 最佳答案

1/x +1/a = a + x(ax)(1/x + 1/a) = ax(a + x)a + x = ax(a + x)ax(a + x) – (a + x) = 0(ax – 1)(a + x) = 0x = 1/a or x = -a

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myisland8132

2010-12-05 1:29 am

(1/x)+(1/a)=a+x Rearranging
x-(1/x)=(1/a)-a
So one solution is -a,. By inspection, the other solution is 1/a.
Finally,the equation can be arranged as x^2-[(1/a)-a]x-1=0. By fundamental theorem of algebra. A a polynomial equation of degree n has n solutions. So, there is no more solution of the equation.

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用戶9170

2010-12-05 1:03 am

x = -a or 1/a

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