Question

The product of three numbers in G.P. is 125 and the sum of their products taken in pair is
87. Find them.​

Answer 1

Step-by-step explanation:

sum of product taken two at a time 87 are u sure .

Answer 2

Answer-

If r = 1.9732 then 3 numbers are 2.53 , 5 , 9.866

and If r = 0.5268 then 3 numbers are 9.5 , 5 , 2.634

Step-by-step explanation:

In this question,

We have been given that

Product of three numbers of G.P is 125 and sum of their products taken in pair is 87.

Let three numbers be $\frac{a}{r},\ a,\ ar$

Hence,Product of three number is 125

$\frac{a}{r}.a.ar\ =\ 125$

Therefore $a^{3}\ =\ 125$

$a\ =\ 5$

Since some of their products taken in pairs is 87.

$\frac{a}{r}(a)\ +\ (a)(ar)\ +\ (ar)\frac{a}{r}\ =\ 87$

$\frac{a^{2}}{r}\ +\ a^{2}r\ +\ a^{2}\ =\ 87$

Taking L.C.M we get,

$a^{2}\ +\ a^{2}r^{2}\ +\ a^{2}r\ =\ 87$

Putting the value of a = 5 we get,

$25\ +\ 25r^{2}\ +\ 25r\ =\ 87r$

$25r^{2}\ -\ 62r\ +\25\ =\ 0$

Using shridhanacharya formula we get,

$\frac{-b\ \pm\ \sqrt{b^{2}\ -\ 4ac}}{2a}$

Here b = -62 a=25 c = 25

$\frac{62\ \pm\ \sqrt{(62)^{2}\ -\ 4\times 25\times 25}}{2\times 25}$

$\frac{62\ \pm\ \sqrt{3844\ -2500}}{50}$

$\frac{62\ \pm\ \sqrt{1344}}{50}$

$\frac{62\ \pm\ 36.66}{50}$

On solving r = 1.9732 and 0.5268

if r = 1.9732 then 3 numbers are 2.53 , 5 , 9.866

and if r = 0.5268 then 3 numbers are 9.5 , 5 , 2.634