Question

I just don't get this question

Answer 1

If a , b, c are the roots of 2x^3 + x^2 -7 =0 , then find the value of
\[\huge \sum_{}^{}\left( \frac{ a }{ b } + \frac{ b }{ a }\right)\]

Answer 2

@dan815

Answer 3

@ganeshie8

Answer 4

\(\large \sum \left(\frac{a}{b} + \frac{b}{a}\right) = \left(\frac{a}{b} + \frac{b}{a}\right)+\left(\frac{b}{c} + \frac{c}{b}\right)+\left(\frac{c}{a} + \frac{a}{c}\right)\)

Answer 5

let roots of the equation be a,b,c. Then simplify a/b+b/a+b/c+c/b+a/c+c/a. (by taking lcm). What you get can be found out by using the formulae for relationships between the roots.

Answer 6

how u got that

Answer 7

\[\frac{ a ^{2}b+a ^{2}c+b ^{2}c+b ^{2}a+c ^{2}b+c ^{2}a }{ abc }\]
=\[\frac{ (ab+bc+ac)(a+b+c)-3abc }{ abc }\]

Answer 8

Ok , how u got
∑...............................

Answer 9

\[\sum_{}^{}\frac{ a }{ b }+\frac{ b }{ a }\]
means what ganeshie wrote.

Answer 10

It means: sum of all terms of the form x/y+y/x where x and y are roots.

Answer 11

k , So in summation (a/b + b/a ) where did c come from

Answer 12

here a and b just mean roots. So, as c is also a root, you have to replace a or b by c to know what the other terms of the summation are. I admit that it's a bit unclear though as a and b were already assigned values at the beginning of the question. So I'd suggest you to interpret that as x/y +y/x where x and y are roots of the polynomial. It makes it much clearer.

Answer 13

Okay i will try doing it .