Question

The degree of the homogeneous function z = ax2 + 2hxy + by2 is​

Answer 1

Answer:

According to Euler theorem, x du/dx + y du/dy = nu; where n is degree of the homogeneous equation.

Now,

Z = ax2 + 2hxy + by2

du/dx = 2ax + 2hy

du/dy = 2hx + 2by

L.H.S = x du/dx + y du/dy

x(2ax + 2hy) + y(2hx + 2by)

= 2ax2 + 2hxy + 2hxy + 2by2

= 2(ax2 + 2hxy + by2) = 2z

Thus Euler theorem verified

$\: \:$

Answer 2

Answer:

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Refer To The Attachment. ⬆️