Question

a,b,c,d are in proportion. if b+c=7, a+d=8 and a square + b square +c square + d square =65, then find the value of a,b,c and d​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

a,b,c,d are in continued proportion

⇒

b

a

=

c

b

=

d

c

=k

⇒a=bk,b=ck,c=dk,

To prove a

2

+b

2

+c

2

)(b

2

+c

2

+d

2

)=(ab+bc+cd+)

2

substituting a,b,c

⇒((bk)

2

+(ck)

2

+(dk)

2

)(b

2

+c

2

+d

2

)=(b

2

k+c

2

k+d

2

k)

2

⇒k

2

(b

2

+c

2

+d

2

)(b

2

+c

2

+d

2

)=k

2

(b

2

+c

2

+d

2

)

2

⇒(b

2

+c

2

+d

2

)

2

=(b

2

+c

2

+d

2

)

2

Hence proved.