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# help!!!!!!!!!!

Please give a hint how to solve this algebra problem:- If p and q are roots of the equation:- $x^{2}-a(x-1)+b$ Then find out the value of:- $\frac{1}{p^{2}-ap}+\frac{1}{q^{2}-bq}+\frac{2}{a+b}$

Note by Aman Sharma
2 years ago

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Hi..Write the equation as $$x^2-ax+(b-a)$$ and try finding roots using the Shrredaracharya Formula..Tell me if this worked... · 2 years ago

By shrredaracharya's formula calculations became too much long....(i am still struggling with algebra and can't handle such large equations) well i am trying to solve it in this way:- By the vieta's formula:- $p+q=a,pq=a+b$ Rearranging a bit gives:- $p-a=-q ,q=\frac{a+b}{p}$ Putting the values of p-a ,a+b and q in give expression and manupulating a bit we get:- $\frac{p+q-b}{(a+b)(q-b)}$ Putting the value of p+q:- $\frac{a-b}{(a+b)(q-b)}$ But official answer of this question is 0 i have to somehow prove that a-b=0 .......i think i am doing a mistake somewhere :-( (Thanks for replying) · 2 years ago

Wow @Aman Sharma , you just said that $$2 = \dfrac{1}{2}$$.

Shouldn't it be $$q = \dfrac{a+b}{p}$$ in place of $$\dfrac{p}{a+b}$$ ?

LOL, i can edit that as a moderator, but i want you to know where you actually missed it. So please try it again. · 2 years ago

:-) ..lol.. i typed it wrong sorry....but you can see that after this wrong step each step is correct(i am not still able to solve this problem please help) · 2 years ago

The question is wrong, it should be $$\dfrac{1}{q^2-aq}$$

Then,

$$\dfrac{1}{p^2-ap} + \dfrac{1}{q^2-aq} + \dfrac{2}{a+b}\\ = \dfrac{1}{p(p-a)} + \dfrac{1}{q(q-a)} + \dfrac{2}{pq} \\ = \dfrac{1}{-pq} + \dfrac{1}{-pq} + \dfrac{2}{pq} = 0$$.

Seems logical @Aman Sharma ? · 2 years ago

I saw this problem in an old iit question paper........hard to believe that question is wrong.....anyway thank you so much for helping...you know i wasted almost 3 hours on this question and realy got frustrated........you are doing great job as a moderator as well a problem writer...keep up good work (and thank you so much again) · 2 years ago

I got that question is wrong, because it's really obvious from the first term that because $$p$$ and $$q$$ are roots of that equation, $$p^2-ap +a+b=0$$ and $$q^2-aq+a+b=0$$ . Hence the first term is simply $$\dfrac{1}{p^2-ap} = \dfrac{1}{-(a+b)}$$ . If you want there the zero, then only thing needed is making the 2nd term equal to$$\dfrac{1}{-(a+b)}$$ and that is done by replacing $$b$$ in second term by $$a$$.

and thank you very much for the appreciation, it inspires me to work harder :) · 2 years ago