Math, asked by kavyasweetybattula, 5 months ago

verify eullors theorm for z=ax²+2hxy+by²

Answers

Answered by Rithiesh07
0

Step-by-step explanation:

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

Now, u = 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) = 2u

Thus Euler theorem verified

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