Solve the following differential equation by factorization method. x^{2}-2ax+a^{2}-b^{2}=0

lugreget9 2021-12-18 Answered
Solve the following differential equation by factorization method.
x22ax+a2b2=0
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Piosellisf
Answered 2021-12-19 Author has 40 answers
Step 1
The given quadratic equation is, x22ax+a2b2=0
Step 2
2a is written as, 2a=(a+b)+(a-b) and a2b2=(a+b)(ab)
x2((a+b)+(ab))x+(a+b)(ab)=0
x2(a+b)x(ab)x+(a+b)(ab)=0
x(x-(a+b))-(a-b)(x-(a+b))
(x-(a+b))(x-(a-b))
x-(a+b)=0, x-(a-b)=0
x=(a+b), x=(a-b)
x=a+b, x=a-b
This is the solution of the quadratic equation is, x22ax+a2b2=0
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Louis Page
Answered 2021-12-20 Author has 34 answers
Step 1
Given quadratic equation is x22ax+a2b2=0
Factorizing the given equation is
x2(a+b)x(ab)x+a2b2=0
x(x-(a+b))-(a-b)(x-(a+b))=0
(x-(a+b))(x-(a-b))=0
x=(a+b), (a-b)
Step 2
Hence obtained
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