Math, asked by virlayadav, 4 days ago

1/a+1/b=2/r prove that

Attachments:

Answers

Answered by Kalpesh0099

Answer:

△=

∣

1+a

2 −b

2 2ab

2b

2ab

1−a

2 +b

2 −2a

−2b

2a

1−a

2 −b

2 ∣

Operating R

1 →R

1 +bR

3 ,

=

∣

1+a

2 +b

2 2ab

2b

0 1−a

2 +b

2 −2a

−b(1+a

2 +b

2 )

2a

1−a

2 −b

2 ∣

Taking (1+a

2 +b

2 ) common from R

1 ,

=(1+a

2 +b

2 )

∣

1 2ab

2b

0 1−a

2 +b

2 −2a

−b

2a

1−a

2 −b

2 ∣

Operating R

2 →R

2 −aR

3 ,

=(1+a

2 +b

2 )

∣

1

0 2b

0 1+a

2 +b

2 −2a

−b

a(1+a

2 +b

2 )

1−a

2 −b

2 ∣

Taking (1+a

2 +b

2 ) common from R

2 ,

=(1+a

2 +b

2 )

2 ∣

1

0 2b

0 1+a

2 +b

2 −2a

−b

a(1+a

2 +b

2 )

1−a

2 −b

2 ∣

Now, on expanding along R

1 , we get

=(1+a

2 +b

2 )

2 [(1−a

2 −b

2 )+(2a

2 +2b

2 )]

=(1+a

2 +b

2 )

2 .(1+a

2 +b

2 )

=(1+a

2 +b

2 )

3 .

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1/a+1/b=2/r prove that​

Answers

Answer:

△=

∣

∣

∣

∣

∣

∣

∣

∣

1+a

2

−b

2

2ab

2b

2ab

1−a

2

+b

2

−2a

−2b

2a

1−a

2

−b

2

∣

∣

∣

∣

∣

∣

∣

∣

Operating R

1

→R

1

+bR

3

,

=

∣

∣

∣

∣

∣

∣

∣

∣

1+a

2

+b

2

2ab

2b

0

1−a

2

+b

2

−2a

−b(1+a

2

+b

2

)

2a

1−a

2

−b

2

∣

∣

∣

∣

1/a+1/b=2/r prove that