state the condition if a,b,c,d and e are in continued proportion
Answers
Step-by-step explanation:
MATHS
If a,b,c,d,e are in continued proportion, prove that
(ab+bc+cd+de)
2
=(a
2
+b
2
+c
2
+d
2
)(b
2
+c
2
+d
2
+e
2
).
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ANSWER
a,b,c,d,e are in continued proportion,
⇒
b
a
=
c
b
=
d
c
=
e
d
=k
⇒a=bk,b=ck,c=dk,d=ek
We need to prove (ab+bc+cd+de)
2
=(a
2
+b
2
+c
2
+d
2
)(b
2
+c
2
+d
2
+e
2
) ....(1)
Substituting the values of a,b,c,d in (1)
⇒(b
2
k+c
2
k+d
2
k+e
2
k)
2
=((bk)
2
+(ck)
2
+(dk)
2
+(ek)
2
)(b
2
+c
2
+d
2
+e
2
)
⇒k
2
(b
2
+c
2
+d
2
+e
2
)
2
=k
2
(b
2
+c
2
+d
2
+e
2
)(b
2
+c
2
+d
2
+e
2
)
⇒(b
2
+c
2
+d
2
+e
2
)
2
=(b
2
+c
2
+d
2
+e
2
)
2
As LHS = RHS
Hence, proved.
Answer:
If a, b, c, d and e are in continued proportion, then a/e is equal to
A) a3/b3
B) a4/b4
C) b3/a3
D) b4/a4
Correct Answer:
B) a4/b4
Description for Correct answer:
Since, a,b,c,d and e are in continued proportion
ab=bc=cd=de=>ed=dc=cb=ba
c=b2a [c/b=b/a] d=c2b=b4a2.1b=b3a2
e=d2c=b6a4.ab2=b4a3
ae=a(b4/a3)=a4b4
Step-by-step explanation: