Find three numbers in AP whose sum and product are respectively 21 and 231.
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Answered by
21
Heya !!!
Let three numbers are ( A - D ) , A and ( A + D )
According to question,
Sum of all three numbers = 21
A - D + A + A + D = 21
3A = 21
A = 21/3 = 7
And,
Product of all three numbers = 231
( A - D ) × A ( A + D ) = 231
A ( A² - D² ) = 231
7 ( 49 - D² ) = 231
7D² = 343 - 231
7D² = 112
D² = 112/7
D = ✓16 = +4 or -4
Thus , A = 7 and D = +4 or -4
Hence,
A - D = 7 - 4 = 3
A = 7
A + D = 7 + 4 = 11
The required numbers are ( 3 , 7 , 11 ) or ( 11 , 7 , 3).
★ HOPE IT WILL HELP YOU ★
★
Let three numbers are ( A - D ) , A and ( A + D )
According to question,
Sum of all three numbers = 21
A - D + A + A + D = 21
3A = 21
A = 21/3 = 7
And,
Product of all three numbers = 231
( A - D ) × A ( A + D ) = 231
A ( A² - D² ) = 231
7 ( 49 - D² ) = 231
7D² = 343 - 231
7D² = 112
D² = 112/7
D = ✓16 = +4 or -4
Thus , A = 7 and D = +4 or -4
Hence,
A - D = 7 - 4 = 3
A = 7
A + D = 7 + 4 = 11
The required numbers are ( 3 , 7 , 11 ) or ( 11 , 7 , 3).
★ HOPE IT WILL HELP YOU ★
★
imemoul:
It's really help full. Thank you so much for ur answer.
Answered by
1
Here is your answer
suppose required numbers are a-d,a,a+d
a = 7
a-d* a * a + d = 231
d = 7
numbers are 11,7,3
Hope it helps you ^_^
suppose required numbers are a-d,a,a+d
a = 7
a-d* a * a + d = 231
d = 7
numbers are 11,7,3
Hope it helps you ^_^
:-)
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