Question

sub duplicate ratio of ✓x:✓y​

Answer 1

Answer:

Solution:-

Given:- x:y be the sub-duplicate ratio of (x−a):(y−a)

To prove:- a=

a+y

xy

Proof:-

x:y be the sub-duplicate ratio of (x−a):(y−a), i.e.,

x:y=

x−a

:

y−a

⇒

y

x

=

y−a

x−a

Squaring both sides,

y

2

x

2

=

y−a

x−a

⇒x

2

(y−a)=y

2

(x−a){By cross multiplication}

⇒x

2

y−x

2

a=y

2

x−y

2

a

⇒x

2

y−y

2

x=x

2

a−y

2

a

⇒xy(x−y)=a(x

2

−y

2

)

⇒a=

(x−y)(x+y)

xy(x−y)

⇒a=

(x+y)

xy

Answer 2

Answer:

Solution:-

Given:- x:y be the sub-duplicate ratio of (x−a):(y−a)

To prove:- a=

a+y

xy

Proof:-

x:y be the sub-duplicate ratio of (x−a):(y−a), i.e.,

x:y=

x−a

:

y−a

⇒

y

x

=

y−a

x−a

Squaring both sides,

y

2

x

2

=

y−a

x−a

⇒x

2

(y−a)=y

2

(x−a){By cross multiplication}

⇒x

2

y−x

2

a=y

2

x−y

2

a

⇒x

2

y−y

2

x=x

2

a−y

2

a

⇒xy(x−y)=a(x

2

−y

2

)

⇒a=

(x−y)(x+y)

xy(x−y)

⇒a=

(x+y)

xy