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# Solve the Following Quadratic Equations by Factorization: M/Nx^2+N/M=1-2x - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

#### 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

or

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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#### APPEARS IN

Solution Solve the Following Quadratic Equations by Factorization: M/Nx^2+N/M=1-2x Concept: Solutions of Quadratic Equations by Factorization.
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