Solve Each of the Following Quadratic Equations: a/(x-b)+b/(x-a)=2, x≠ b,a
By BYJU'S Exam Prep
Updated on: October 17th, 2023
Solve each of the following quadratic equations: a/(x-b)+b/(x-a)=2,x≠b,a
To solve the quadratic equation a / (x – b)) + (b / (x – a) = 2, we can follow these steps:
Step 1: Multiply through by (x – b)(x – a) to eliminate the denominators.
Step 2: Expand and simplify the equation thus obtained. Then we will combine like terms
Step 3: On further solving, we will obtain two solutions for the equation.
Table of content
Solve Each of the Following Quadratic Equations: a/(x-b)+b/(x-a)=2,x≠b,a
Solution:
Given the equation:
(a / (x – b)) + (b / (x – a)) = 2
To simplify the equation, we can find a common denominator:
[(a(x – a)) + (b(x – b))] / ((x – b)(x – a)) = 2
Expanding and simplifying the equation:
(ax – a² + bx – b²) = 2 ((x – b)(x – a))
(ax – a² + bx – b²) = 2x²–2ax–2bx+2ab
Rearranging the equation to bring all terms to one side:
2x² – 3x(a + b) + (a + b)² = 0
Expanding the middle term:
2x² – 2x(a + b)- x(a + b) + (a + b)² = 0
Combining like terms:
2x(x- (a + b)) – (a + b)(x- (a + b))= 0
Simplifying further:
(2x- (a + b))(x- (a + b))= 0
x = (a+b/2) and x = (a+b)
Answer:
On Solving Each of the Following Quadratic Equations: a/(x-b)+b/(x-a)=2, we get x=(a+b/2) and x=(a+b)
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