if the ratio a:bis unaltered when x and yare added to its items in order show that x:y =a:b
Answers
Answer:
Positive number a,b
A.M=
2
a+b
GM=
ab
m:n=
2
ab
a+b
R.H.S=
(m−
m
2
−n
2
)
(m+
m
2
−n
2
)
Divide by n in both numerator and denominator.
=
(
n
m
−
n
2
m
2
−1
)
(
n
m
+
n
2
m
2
−1
)
=
(
2
ab
a+b
−
4ab
a
2
+b
2
+2ab
−1
)
(
2
ab
a+b
+
4ab
a
2
+b
2
+2ab
−1
)
=
(
2
ab
a+b
−
4ab
a
2
+b
2
−2ab
)
(
2
ab
a+b
+
4ab
a
2
+b
2
−2ab
)
=
2
ab
a+b+(a−b)
2b
2a
=
b
a
=LHS
LHS=RHS
Answer:
Positive number a,b
A.M=
2
a+b
GM=
ab
m:n=
2
ab
a+b
R.H.S=
(m−
m
2
−n
2
)
(m+
m
2
−n
2
)
Divide by n in both numerator and denominator.
=
(
n
m
−
n
2
m
2
−1
)
(
n
m
+
n
2
m
2
−1
)
=
(
2
ab
a+b
−
4ab
a
2
+b
2
+2ab
−1
)
(
2
ab
a+b
+
4ab
a
2
+b
2
+2ab
−1
)
=
(
2
ab
a+b
−
4ab
a
2
+b
2
−2ab
)
(
2
ab
a+b
+
4ab
a
2
+b
2
−2ab
)
=
2
ab
a+b+(a−b)
2b
2a
=
b
a
=LHS
LHS=RHS
Answer:
Positive number a,b
A.M=
2
a+b
GM=
ab
m:n=
2
ab
a+b
R.H.S=
(m−
m
2
−n
2
)
(m+
m
2
−n
2
)
Divide by n in both numerator and denominator.
=
(
n
m
−
n
2
m
2
−1
)
(
n
m
+
n
2
m
2
−1
)
=
(
2
ab
a+b
−
4ab
a
2
+b
2
+2ab
−1
)
(
2
ab
a+b
+
4ab
a
2
+b
2
+2ab
−1
)
=
(
2
ab
a+b
−
4ab
a
2
+b
2
−2ab
)
(
2
ab
a+b
+
4ab
a
2
+b
2
−2ab
)
=
2
ab
a+b+(a−b)
2b
2a
=
b
a
=LHS
LHS=RHS