Find three numbers in G.P. whose sum is 65 and whose product is 3375.

Asked by Aaryan | 1 year ago |  57

##### Solution :-

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

So, according to the question

$$\dfrac{a}{r} + a + ar = 65$$… equation (1)

$$\dfrac{a}{r} + a + ar = 3375$$ … equation (2)

From equation (2) we get,

a3 = 3375

a = 15.

From equation (1) we get,

$$\dfrac{ (a + ar + ar^2)}{r}$$ = 65

a + ar + ar2 = 65r … equation (3)

Substituting a = 15 in equation (3) we get

15 + 15r + 15r2 = 65r

15r2 – 50r + 15 = 0… equation (4)

Dividing equation (4) by 5 we get

3r2 – 10r + 3 = 0

3r2 – 9r – r + 3 = 0

3r(r – 3) – 1(r – 3) = 0

r = 3 or r = $$\dfrac{1}{3}$$

Now, the equation will be

$$\dfrac{15}{3}$$, 15, 15×3 or

So the terms are 5, 15, 45 or 45, 15, 5

The three numbers are 5, 15, 45.

Answered by Sakshi | 1 year ago

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