SOLUTION: 1. If x + a/x = b then find the value of (x^2 + bx + a)/(bx^2 - x^3) 2. If x + 1/x = 99, find the value of 100x/(3x^2 + 103x + 3) Question from Tata Mc Graw-Hill NTSE b

Question 110861: 1. If x + a/x = b then find the value of (x^2 + bx + a)/(bx^2 - x^3)
2. If x + 1/x = 99, find the value of 100x/(3x^2 + 103x + 3)

Question from Tata Mc Graw-Hill NTSE book
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
x + a/x = b
(x^2 + bx + a)/(bx^2 - x^3)
(x^2+x(x + a/x)+a/(x^2(x + a/x )-x^3
(x^2+x^2 + a +a)/(x^3 + ax -x^3)
(2x^2+2a)/ax
.
x + 1/x = 99
x^2+1=99x eliminate fractions multiply each side by x
x^2-99x+1=0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=9797 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 98.9898979590785, 0.0101020409215238. Here's your graph:

I'll let you plug the answers for x into the equation below to get the answers which should both be .25
100x/(3x^2 + 103x + 3)
.
Ed

RELATED QUESTIONS
given that x=3+i is a root of p(x)=3x^4+ax^3+34x^2+bx-20 find the value of a and b if... (answered by greenestamps)

If {{{ x^3+5x-10=0 }}} Then find the value of {{{ x^7+100x^2+25x... (answered by ikleyn,greenestamps)

IF (x-5)(x^2-6x+4) = Ax^3 + Bx^2 + Cx + D, find the value of... (answered by Edwin McCravy)

find the values of A, B and C if (x-1), (x+2), and (x-2) are factors of... (answered by greenestamps)

ax^3+bx^2+x-6 has factor (x+2) and (x-2) then in both cases remainder is 4 then find the... (answered by josgarithmetic)

Find the sum of a, b, c, and d if (x^3 - 2x^2 + 3x + 5)/(x + 2) = ax^2 + bx + c +... (answered by josgarithmetic,timofer)

find the values of A,B,C if (x-1),(x+2) and (x-2) are factor of... (answered by ikleyn,math_tutor2020)

find b such that f(x)=-4x^2+bx+3 has a maximum value of... (answered by ankor@dixie-net.com)

Find the value of the constants A, B, C and D in the following identity: {{{... (answered by Fombitz)