What will be the difference of the roots of this given equation?

Question

What will be the difference of the roots of the equation $$ (x^2 - 10x - 29)^{-1} + (x^2 - 10x - 45)^{-1} = 2(x^2 - 10x - 69)^{-1} $$

I actually tried to solve it but it was too lengthy to calculate with the simple method I know. I want to solve it in less time coz someone told me that it could be solved in less time. Can someone help?

Thanks a lot, I got y = 39, and the roots as -3 and 13, so the difference of the roots = 16. — Resorcinol, Jan 08 '17 at 02:17
@dxiv Thanks a lot, I got y = 39, and the roots as -3 and 13, so the difference of the roots = 16. — Resorcinol, Jan 08 '17 at 02:19

Arnaldo · Accepted Answer · 2017-01-08T02:20:32.217

2

$$x^2-10x-45=y$$ then

$$\frac{1}{y+16}+\frac{1}{y}=\frac{2}{y-24}$$

$$(2y+16)(y-24)=(y+16)2y \rightarrow y=-6 $$

Can you finish?

edited Jan 08 '17 at 02:20

answered Jan 08 '17 at 02:15

Arnaldo

21,342

Thanks I got y = -6 and the difference of the roots to be 16 – Resorcinol Jan 08 '17 at 02:23
The roots are -3 and 13 – Resorcinol Jan 08 '17 at 02:25
You are very welcome! – Arnaldo Jan 08 '17 at 02:26

What will be the difference of the roots of this given equation?

1 Answers1