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Algebra and Applications Test 2

Question : 2 of 40

Marks: +1, -0

\frac{1}{m}+\frac{1}{n}+\frac{1}{o}=\frac{1}{m+n+o}

m + n + o \neq 0, mno \neq 0

(m + n)(n + o)(o + m)

Solution: 👈: Video Solution

Concept:

Use expansion and factorisation to connect the given equation with the required product.

Explanation:

Given:

\frac{1}{m}+\frac{1}{n}+\frac{1}{o}=\frac{1}{m+n+o}

Combine the left side:

\frac{mn+no+om}{mno}=\frac{1}{m+n+o}

Cross-multiply:

(mn+no+om)(m+n+o)=mno

Expand the left side:

(mn+no+om)(m+n+o)=m^2n+mn^2+n^2o+no^2+m^2o+mo^2+3mno

So,

m^2n+mn^2+n^2o+no^2+m^2o+mo^2+2mno=0

Now expand the required product:

(m+n)(n+o)(o+m)=m^2n+mn^2+n^2o+no^2+m^2o+mo^2+2mno

Thus,

(m+n)(n+o)(o+m)=0

Answer:

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