Math, asked by sam200314, 5 months ago

Z - (x²+y2 +xy) verify Euler's theorem​

Answers

Answered by lakshaya98
0

Answer:

Euler's theorem

f(x,y)=

x

2

+y

2

1

f(tx,ty)=

t

2

x

2

+t

2

y

2

1

=

t

1

.f(x,y)=t

−1

f(x,y)

∴ f is a homogeneous function of degree −1 and by Euler's theorem

x

∂x

∂f

+y

∂y

∂f

=−f

Verification:

∂x

∂f

=

2

−1

.

(x

2

+y

2

)

3/2

2x

=

(x

2

+y

2

)

3/2

−x

Similarly

∂y

∂f

=

(x

2

+y

2

)

3/2

−y

x

∂x

∂f

+y

∂y

∂f

=−(

(x

2

+y

2

)

3/2

x

2

+y

2

)

x

2

+y

2

−1

=−f

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Answered by bunty143
0

Answer:

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