Solve the Following Quadratic Equations by Factorization: `M/Nx^2+N/M=1-2x`

Question

Solve the following quadratic equations by factorization:

`m/nx^2+n/m=1-2x`

Solution

We have been given

`m/nx^2+n/m=1-2x`

`(m^2x^2+n^2)/(mn)=1-2x`

m2x2 + 2mnx + (n2 - mn) = 0

`m^2x^2+mnx+mnx+[n^2-(sqrt(mn))^2]=0`

`m^2x^2+mnx+mnx+(n+sqrt(mn))(n-sqrt(nm))+(msqrt(mnx)-msqrt(mnx))=0`

`[m^2x^2 + mnx + msqrt(mnx)]+[mnx-msqrt(mnx)+(n+sqrt(mn))(n-sqrt(mn))]=0`

`[m^2x^2 + mnx + msqrt(mnx)]+[(mx)(n-sqrt(mn))+(n+sqrt(mn))(n-sqrt(mn))]=0`

`(mx)(mx+n+sqrt(mn))+(n-sqrt(mn))(mx+n+sqrt(mn))=0`

`(mx+n+sqrt(mn))(mx+n-sqrt(mn))=0`

Therefore,

`mx+n+sqrt(mn)=0`

`mx=-n-sqrt(mn)`

`x=(-n-sqrt(mn))/m`

`mx+n-sqrt(mn)=0`

`mx=-n+sqrt(mn)`

`x=(-n-sqrt(mn))/m`

Hence, `x=(-n-sqrt(mn))/m` or `x=(-n-sqrt(mn))/m`

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Method of Solving a Quadratic Equation

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Q 44 Q 43 Q 45

Chapter 4: Quadratic Equations - Exercise 4.3 [Page 20]

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R.D. Sharma Mathematics [English] Class 10

Chapter 4 Quadratic Equations
Exercise 4.3 | Q 44 | Page 20

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