Algebra and Applications Test 1

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Question : 34 of 40

Marks: +1, -0

If l, m and n are unequal natural numbers such that

l ^2 = mn

, consider the following:
1.

{l+n}/n={m+l}/l

2.l/{n-l}=m/{l-m}

3.{l+n}/{n-l}={m+l}/{l-m}

Which of the above statement(s) is/are correct?

1 and 2 only
2 and 3 only
1 and 3 only
1, 2 and 3
None of these

Solution:

∵ l≠m≠n

and

l^2=mn

1.

{l+n}/n={m+l}/l

⇒l^2+ln=mn+ln

⇒l^2=mn

2.l/{n-l}=m/{l-m}

⇒l^2-lm=mn-lm

⇒l^2=mn

3.{l+n}/{n-l}={m+l}/{l-m}

⇒l^2-lm+ln-mn=mn+ln-lm-l^2

⇒l^2=mn

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