lugreget9
2021-12-18
Answered

Solve the following differential equation by factorization method.

${x}^{2}-2ax+{a}^{2}-{b}^{2}=0$

You can still ask an expert for help

Piosellisf

Answered 2021-12-19
Author has **40** answers

Step 1

The given quadratic equation is,${x}^{2}-2ax+{a}^{2}-{b}^{2}=0$

Step 2

2a is written as, 2a=(a+b)+(a-b) and${a}^{2}-{b}^{2}=(a+b)(a-b)$

${x}^{2}-((a+b)+(a-b))x+(a+b)(a-b)=0$

${x}^{2}-(a+b)x-(a-b)x+(a+b)(a-b)=0$

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,${x}^{2}-2ax+{a}^{2}-{b}^{2}=0$

The given quadratic equation is,

Step 2

2a is written as, 2a=(a+b)+(a-b) and

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,

Louis Page

Answered 2021-12-20
Author has **34** answers

Step 1

Given quadratic equation is${x}^{2}-2ax+{a}^{2}{b}^{2}=0$

Factorizing the given equation is

${x}^{2}-(a+b)x-(a-b)x+{a}^{2}-{b}^{2}=0$

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

Given quadratic equation is

Factorizing the given equation is

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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