English paper ncert class 10 2021 batao yaar Kal paper hai
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Answer:
Let
h(x)=maximum value=8xyz+f(x2/a2+y2/b2+z2/C2+1)
where f =langragian multiplier.
Then differintiate partialy with respect to x
8yz+2fx/a2=0
1/a2=(−8yz/2fx)
similarily
1/b2=(−8zx/2fy)
1/c2=(−8xy/2fz)
x2/a2+y2/b2+z2/c2=1
⇒f=−12xyz
put f value in eqn(2)
x=a/
√
3
similarily
y=b/
√
3
z=c/
√
3
⇒ the largest volume of parallelopiped inscribed in ellipsoid
=8xyz=8(a/
√
3
)(b/
√
3
)(c/
√
3
Explanation:
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