three numbers are in a. p. if their sum is -3 and product is 8,find their numbers...ques no 39
Answers
Answer :
Let numbers be a , a + d , a + 2d
Sum = -3
a + a + d + a +2d = -3
3a + 3d = -3
3 ( a + d) = -3
a + d = -1................ ( 1 )
Product = 8
a × ( a + d ) × ( a + 2d ) = 8
Putting values from eq 1
a = -1 -d
(-1 - d ) × -1 × ( -1 -d + 2d ) = 8 ........ { a + d = -1}.....
-1(-1-d) × (-1 + d) = 8
(d + 1) ×( d - 1) = 8
.............{ Using identity .... ( a + b ) ( a - b) = a^2 - b^2.}
d ^2 - 1 ^2 = 8
d^2 = 8 +1 =9
d^2 = 9
d = √9
d =+/ - 3.
Putting d = 3 in eq 1.
a + 3 = -1
a = -1 -3 = -4.
Now,
a = -4
a + d = -4 + 3 = -1
a + 2d = -4 + 2×3 = -4 +6= 2.
Numbers are =
-4 , -1 , 2....
Putting d = -3
We get ....
a = -1 - (-3)
= -1 + 3
= 2
a + d = 2 + (-3)
= -1
a + 2d = 2 + 2×(-3)
= 2 + (-6)
= -4
There fore .....Numbers will be
-4 , -1 ,2
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