Question

verify Euler's theorem, when
f(x,y,z)=xy+yz+zx​

Answer 1

Answer:

$\huge\boxed{\fcolorbox{green}{purple}{Answer}}$

❥━━━━━━━━❥

i. Species is the group of organisms that can produce fertile individuals through natural reproduction.

ii. Each species grows in specific geographical conditions. Their food, habitat, reproductive ability and

period is different.

iii.However, genetic variation is responsible for formation of new species from earlier one. Besides,

geographical and reproductive changes are also responsible.

iv.

Similarly, geographical or reproductive isolation also leads to speciation which is the result of

evolution of the new species which survival modifications.

v. Therefore, Formation of new species of plants and animals is the effect of evolutio

Answer 2

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