Question

The geometric mean of two numbers a and b is 8 and their harmonic mean is 6.4. The numbers are

• A. 2, 8
• B. 4, 16
• C. 4, 8
• D. 2, 16

Answer 1

The correct option is B 4, 16

$By$ $hypothes,$ $\sqrt{ab}=8$
or $ab=64$ ......(i)
$\frac{2ab}{a+b}=6.4$
$From$ $equation\left(i\right)$
$2\times 64=6.4(a+b)$
or $a+b=20$ ......(ii)
or $b=20-a$
$Substituting$ $the$ $value$ $of$ $b$ $in$ $equation\left(i\right),$
$a(20-a)=64$
or $a^2-20a+64=0$
or $(a-16)(a-4)=0$
$\therefore a=16$ or $a=4$
$From$ $equation\left(ii\right)$
$b=20-16$
or $20-4=4$ or 16
$Hence,$ $the$ $numbers$ $are4,16.$