Find three number in G.P. whose sum is 38 and their product is 1728.

Asked by Aaryan | 1 year ago |  52

##### Solution :-

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

So, according to the question

$$\dfrac{a}{r} + a + ar = 38$$ … equation (1)

$$\dfrac{a}{r} + a + ar = 1728$$ … equation (2)

From equation (2) we get,

a3 = 1728

a = 12.

From equation (1) we get,

$$\dfrac{ (a + ar + ar^2)}{r}$$ = 38

a + ar + ar2 = 38r … equation (3)

Substituting a = 12 in equation (3) we get

12 + 12r + 12r2 = 38r

12r2 – 26r + 12 = 0… equation (4)

Dividing equation (4) by 2 we get

6r2 – 13r + 6 = 0

6r2 – 9r – 4r + 6 = 0

3r(3r – 3) – 2(3r – 3) = 0

r = $$\dfrac{3}{2}$$

Now the equation will be

($$\dfrac{12}{ \dfrac{3}{2}}$$) = 8 or

So the terms are 8, 12, 18

The three numbers are 8, 12, 18

Answered by Sakshi | 1 year ago

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