Question

The harmonic mean and geometric mean of two values are 6.4 and 8 respectively. The values are

Answer 1

Answer:

a=16 and b=4 or a=4 and b=16

Step-by-step explanation:

Let a and b are two numbers

Harmonic mean=6.4

Geometric mean=8

$H.M=\frac{2}{\frac{1}{a}+\frac{1}{b}}$

$\frac{2ab}{a+b}=6.4$

$G.M=\sqrt{ab}=8$

$ab=64$

Squaring on both sides

Substitute the values then we get

$\frac{2\cdot64}{a+b}=6.4$

$a+b=\frac{64\cdot2\times 10}{64}$

$a+b=20$

$b=20-a$

$ab=64$

$a(20-a)=64$

$20a-a^2=64$

$a^2-20a+64=0$

$a^2-16a-4a+64=0$

$(a-16)(a-4)=0$

a=16 and a=4

b=20-16=4 and b=20-4=16