Question

Solve for x , by factorisation method:
(m/n) x^2 + n/m = 1 - 2x

Answer 1

(m/n)x² +(n/m) = 1 -2x

(m/n)x² +n/m -1 +2x =0

m²x² + n² -mn + 2mnx =0

m²x² +2mnx +( n² -mn) =0

(m²x² +2mnx +n²) -mn =0

(mx + n)² -mn =0

(mx + n)² = mn
take square root both sides

(mx + n)= ±√mn

mx = -n ±√mn

x ={ -n±√mn}/m
={ -n/m ±√(n/m) }

Answer 2

(m/n)x^2 + 2x + n/m=1

=>m^x^2+2mnx+n^2
_________________ = 1
mn

=>m^2x^2+2mnx+n^2=mn

=>(mx+n)^2=mn

=>mx+n=+-_/mn
So,
x=(+-_/mn - n)/m

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