Solving Equations Worksheet1 Solution1





In this page solving equations worksheet1 solution1 we are going to see solution of practice questions.

Question 1:

If (x/b) + (b/x) = (a/b) + (b/a) the roots of the equation are

Solution:

(x/b) + (b/x) = (a/b) + (b/a)

First we are going to take L.C.M for both fractions

[(x² + b²)/bx] = (a² + b²)/ab

ab (x² + b²) = bx (a² + b²)

ab x² + a b³ = a²b x + b³ x

ab x² + a b³ - a²b x - b³ x = 0

ab x² + (-a²b- b³) x + a b³ = 0

we are going to solve this quadratic equation by quadratic formula

a = ab   b = (-a²b- b³)    c = a b³

 x = [- b ± √(b² - 4 a c)]/2 a

 x = [(a²b+b³) ± √(a²b+b³)² - 4 (ab) (a b³)]/2(ab)

 x = [(a²b+b³) ± √(a⁴ b² + 2 a² b⁴ + b⁶ - 4 a² b⁴)]/2ab

 x = [(a²b+b³) ± √(a⁴ b² + b⁶ - 2 a² b⁴)]/2ab

 x = [(a²b+b³) ± √(a² b)² + (b³)² - 2 a²b (b³)]/2ab

 x = [(a²b+b³) ± √(a² b - b³)²]/2ab

 x = [(a²b+b³) ± (a² b - b³)]/2ab

 x = [(a²b+b³) + (a² b - b³)]/2ab    x = [(a²b+b³) - (a² b - b³)]/2ab

 x = [a²b+b³+a² b- b³]/2ab    x = [a²b+b³-a² b+b³]/2ab

 x = (2a²b)/2ab    x = (2b³)/2ab

 x = a    x = b²/a

(A)  a,b²/a

(B)  a²,b/a²

(C)  a²,b²/a

(D)  a,b²

solving equations worksheet1 solution1 solving equations worksheet1 solution1