please answer by solving pleaseThe arthrmatic mean and geometric mean two numbers are in ratio 5 ratio 3 and the sum of two number 40. then they are About the author Luna
Answer: Explanation: [tex]\huge\red{✡}✡ \huge\blue{✡ } ✡ \huge\pink{ ✡}✡ \huge \purple{✡} ✡ \huge\red{✡}✡ \huge\blue{✡ } ✡ \huge\pink{ ✡}✡ \huge \purple{✡} ✡ \huge\red{✡}✡ \huge\blue{✡ } ✡ \huge\pink{ ✡}✡ \huge \purple{✡} ✡ \huge\red{✡}✡ \huge\blue{✡ } ✡ \huge\pink{ ✡}✡ \huge \purple{✡} ✡ \huge\red{✡}✡ \huge\blue{✡ } ✡ \huge\pink{ ✡}✡ \huge \purple{✡}[/tex] Reply
Answer: Correct option is A 1:4 B 4:1 Let a,b be two numbers which are in H.P and G.P. a,b are in H.P implies HM = a+b 2ab a,b are in G.P. implies GM = ab Therefore, ab a+b 2ab = 5 4 ⇒( a+b 2ab )5=4 ab ⇒ ab =( a+b 2ab ) 4 5 ⇒ ab =( 4(a+b) 10ab ) ⇒4(a+b)=10 ab ⇒ ab 4(a+b) =10 ⇒4( ab a + ab b )=10 ⇒( b a + a b )= 2 5 Let b a =t then a b = t 1 . So, t+ t 1 = 2 5 ⇒ t t 2 +1 = 2 5 ⇒t 2 − 2 5t +1=0 ⇒2t 2 −5t+2=0 ⇒2t 2 −4t−t+2=0 ⇒t=2 or ⇒t= 2 1 Therefore, b a = 1 4 or b a = 4 1 . Reply
Answer:
Explanation:
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Answer:
Correct option is
A
1:4
B
4:1
Let a,b be two numbers which are in H.P and G.P.
a,b are in H.P implies HM =
a+b
2ab
a,b are in G.P. implies GM =
ab
Therefore,
ab
a+b
2ab
=
5
4
⇒(
a+b
2ab
)5=4
ab
⇒
ab
=(
a+b
2ab
)
4
5
⇒
ab
=(
4(a+b)
10ab
)
⇒4(a+b)=10
ab
⇒
ab
4(a+b)
=10
⇒4(
ab
a
+
ab
b
)=10
⇒(
b
a
+
a
b
)=
2
5
Let
b
a
=t then
a
b
=
t
1
.
So, t+
t
1
=
2
5
⇒
t
t
2
+1
=
2
5
⇒t
2
−
2
5t
+1=0
⇒2t
2
−5t+2=0
⇒2t
2
−4t−t+2=0
⇒t=2 or ⇒t=
2
1
Therefore,
b
a
=
1
4
or
b
a
=
4
1
.