Question

if a:b :: c:d show that a+b/c+d= √2a2 + 7b2/ √2c2+7d2


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Answer 1

Answer:

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Step-by-step explanation:

If a,b,c,d are in proportion, then prove that

b

2

+5d

2

a

2

+5c

2

=

b

a

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ANSWER

Given a,b,c and d are in proportion

b

a

=

d

c

−−−−−−−(1)

ad=bc

a=

d

bc

b

2

+5d

2

a

2

+5c

2

=

b

a

⇒

b

2

+5d

2

(

d

bc

)

2

+5c

2

⇒

b

2

+5d

2

d

2

b

2

c

2

+5c

2

⇒

b

2

d

2

+5d

4

b

2

c

2

+5c

2

d

2

⇒

d

2

(b

2

+5d

2

)

c

2

(b

2

+5d

2

)

⇒

d

2

c

2

=

d

c

⇒

b

2

+5d

2

a

2

+5c

2

=

d

c

From (1)

⇒

d

c

=

b

a

∴

b

2

+5d

2

a

2

+5x

2

=

b

a