three numbers in AP whose sum is 36 and the product is 1680 find the numbers
Answers
Answer:
are 5,12,19.
Step-by-step explanation:
Given : The sum of three numbers in AP is 36 and their product is 1140.
To find : The three numbers in AP ?
Solution :
Let the three numbers in A.P be (a-d), a and (a+d) respectively.
The sum of three numbers in AP is 36.
a-d+a+a+d=36a−d+a+a+d=36
3a=363a=36
a=\frac{36}{3}a=
3
36
a=12a=12
Product of three numbers is 1140.
(a-d)\times(a)\times (a+d)=1140(a−d)×(a)×(a+d)=1140
a(a^2-d^2)=1140a(a
2
−d
2
)=1140
12(12^2-d^2)=114012(12
2
−d
2
)=1140
144-d^2=\frac{1140}{12}144−d
2
=
12
1140
144-d^2=95144−d
2
=95
d^2=144-95d
2
=144−95
d^2=49d
2
=49
d=\sqrt{49}d=
49
d=\pm 7d=±7
When a=12 and d=7,
a-d=12-7=5
a=12
a+d=12+7=19
When a=12 and d=-7,
a-d=12-(-7)=19
a=12
a+d=12-7=5
Therefore, the three numbers in A.P are 5,12,19.
Step-by-step explanation:
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