Question

three numbers are in AP whose sum is 33 and product is 792 10 the smallest number for this number is ​

Answer 1

Answer:

4

Step-by-step explanation:

Let the numbers be (a-d) , a , (a+d) {where a is the first term and d is common difference}

ATQ,

a-d + a + a+d = 33

3a=33

a= 11

Hence,

(11-d) x (11) x (11+d) = 792

(121 - d²)= 792/11

121-d² = 72

d²= 49

d= ±7

CASE I- (when d = +7)

AP- 4, 11 , 18

CASE II-(when d = -7)

AP- 18 , 11 , 4

∴ smallest number = 4

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Answer 2

Answer:

Let a-d, a, a+d be the 3 numbers in AP.

Sum = a-d+a+a+d = 33

3a = 33

a = 11

Product, (a-d)a(a+d) = 792

(11-d)11(11+d) = 792

121-d² = 792/11

121-d² = 72

121-72 = d2

So d² = 49

d = ±7

So 4, 11, 18 or 18, 11, 4 are the numbers.

Smallest number is 4.