Solve each of the following quadratic equations: a/ (x – b) + b/ (x – a) = 2, x ≠ b, a

By BYJU'S Exam Prep

Updated on: September 25th, 2023

By solving each of the following quadratic equations a/ (x – b) + b/ (x – a) = 2, x ≠ b, a, we get x = a + b/2 or x = a + b. Steps to solve the given Quadratic equation:

Given that a/ (x – b) + b/ (x – a) = 2

[a (x – a) + b (x – b)]/ (x – a) (x – b) = 2

On multiplying we get:

ax – a2 + bx – b2 = 2×2 – 2ax – 2bx + 2ab

On rearranging we get:

2×2 – 2ax – ax – 2bx – bx + a2 + b2 + 2ab = 0

Simplifying the above equation we get:

2×2 – 3x (a + b) + (a + b)2 = 0

2×2 – 2x (a + b) – x (a + b) + (a + b)2 = 0

Taking common:

2x (x – (a + b)) – (a + b) (x – (a + b)) = 0

(2x – (a + b)) (x – (a + b)) = 0

x = a + b/2 or x = a + b

Table of content

1. Solve each of the following quadratic equations: a/ (x – b) + b/ (x – a) = 2, x ≠ b, a

Quadratic Equation

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:

ax² + bx + c = 0

where a, b, and c are numerical coefficients and x is an unknown variable. For instance, x2 + 2x +1 is a quadratic or quadratic equation. Here, a ≠ 0 due to the fact that if it equals 0, the equation will cease to be quadratic and change to a linear equation, such as:

bx+c=0

As a result, we cannot refer to this equation as a quadratic equation. Another name for the terms a, b, and c is quadratic coefficients. The values of the unknown variable x that fulfill the quadratic equation are the solutions to the problem. Quadratic equations’ roots or zeros are known as these solutions. The answers to the given equation are the roots of any polynomial.

Summary: