Question

Find three numbers in ap whose sum is 21 and their product is 231

Answer 1

Answer:

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Step-by-step explanation:

the three numbers will be (a-d), a , (a+d)

then (a-d)+a+(a+d) = 21

3a = 21

a = 7

then (a-d)(a)(a+d) = 231

( a²-ad)(a+d) = 231

a³+a²d - a²d - ad² = 231

a³ - ad² = 231

(7)³ - (7)d² = 231

343 - 7 d² = 231

- 7d² = - 112

7d² = 112

d² = 16

d = 4

then a-d = 7-4 = 3

a = 7

a+d = 7+4 = 11

the three numbers are 3 , 7 , 11

Answer 2

Answer:

7,11,15,.....

Step-by-step explanation:

Let the number be (a-d), a, (a+d)

(a-d)+a+(a+d)=21

a-d+a+a+d=21

3a=21

a=7

(a-d)(a)(a+d)=231

(a²-d²)7=231

a²-d²=33

7²-d²=33

49-d²=33

d²=49-33

d²=16

d=4

hence,the numbers are 7,11,15,....