The arithmetic mean of two numbers is 10 and their geometric mean is 8. Find the numbers.
Answers
Answered by
2
Step-by-step explanation:
Let the numbers be a, b.
So, arithmetic mean =
a
+
b
2
⟹
a
+
b
2
= 10
⟹
a+b = 20.
Geometric mean =
√
a
b
⟹
√
a
b
= 8
⟹
ab = 64.
Since a+b = 20
⟹
b = 20-a
⟹
a
×
(20-a) = 64
⟹
a
2
-20a+64 = 0
⟹
a
2
-16a-4a+64 = 0
⟹
(a-16)
×
(a-4) =0
⟹
a= 16 or a= 4.
So, the numbers are 16, 4.
Answered by
2
Answer:
Let the numbers be a, b.
So, arithmetic mean =
a
+
b
2
⟹
a
+
b
2
= 10
⟹
a+b = 20.
Geometric mean =
√
a
b
⟹
√
a
b
= 8
⟹
ab = 64.
Since a+b = 20
⟹
b = 20-a
⟹
a
×
(20-a) = 64
⟹
a
2
-20a+64 = 0
⟹
a
2
-16a-4a+64 = 0
⟹
(a-16)
×
(a-4) =0
⟹
a= 16 or a= 4.
So, the numbers are 16, 4.
Step-by-step explanation:
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