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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The H.P. of two numbers is $4$ and the arithmetic mean $A$ and geometric mean $G$ satisfy
$2A+G^2=27$. The numbers are
Solution
If numbers are $a,b$:
H.P. $=\dfrac{2ab}{a+b}=4 \Rightarrow ab=2(a+b)$
$A=\dfrac{a+b}{2},\quad G^2=ab$
Given:
$2A+G^2=(a+b)+ab=27$
Substitute $ab=2(a+b)$:
$3(a+b)=27 \Rightarrow a+b=9$
$ab=18$
So numbers are roots of
$x^2-9x+18=0 \Rightarrow x=6,3$
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