Question

A.M and G.M of two numbers are 226/50 and 3/5 respectively. Find the numbers.​

Answer 1

Answer:

Let the no.s be “a” and “b”, So, (a+b)/2 =3.2 and √(ab)=4 (just using the arithmetic mean and geometric mean data) so , a+b=6.4 and √ ab= ...

Answer 2

The correct answer is (a, b) is $(9,\frac{1}{25} )$ or $(\frac{1}{25},9 )$.

Given: The AM of two numbers = $\frac{226}{50}.$

The GM of two numbers = $\frac{3}{5}$.

To Find: The numbers.

Solution:

AM of two numbers a and b is = $\frac{a+b}{2}$.

$\frac{a+b}{2}=\frac{226}{50}$

$a+b=\frac{226}{25}$

$b=\frac{226}{25}-a$  (equation 1)

GM of two numbers a and b is = $\sqrt{ab}$

$\sqrt{ab}=\frac{3}{5}$

Squaring both the sides.

$ab=\frac{9}{25}$

Put the value of b from equation 1.

$a(\frac{226}{25}-a) =\frac{9}{25}$

$\frac{226}{25}a-a^{2} =\frac{9}{25}$

$226a-25a^{2} =9$

$25a^{2} -226a+9=0$

$25a^{2} -225a-a+9=0\\ 25a(a-9)-1(a-9)$

= (25a-1)(a-9)

a = 9 and $\frac{1}{25}$.

$b=\frac{226}{25}-a$

For a = 9, $b=\frac{226}{25}-9=\frac{226-225}{25}=\frac{1}{25}$.

For a = $\frac{1}{25}$, $b=\frac{226}{25}-\frac{1}{25}=9$

Hence, (a, b) is $(9,\frac{1}{25} )$ or $(\frac{1}{25},9 )$.

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