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Special Determinants

if the three ...

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if the three positive numbers a,b,c are in AP and 1/a^2,1/b^2,1/c^2 also in AP then

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(b + c) (c + a) (a + b)

are in H.P., then show that

\frac{1}{a^{2}}, \frac{1}{b^{2}}, \frac{1}{c^{2}}

are also in H.P

a^{2}, b^{2}, c^{2}

A P

\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{b + a}

A P .

Q. For three numbers

a, b, c

product of the average of the numbers,

a^{2}, b^{2}, c^{2}

\frac{1}{a^{2}}, \frac{1}{b^{2}}, \frac{1}{c^{2}}

cannot be less than

a, b, c, d

are real numbers and

a^{2}, b^{2}, c^{2}

A P

then which of the following combinations are in

A P

.

Q. If three positive real numbers

a, b, c

a b c = 4

, then the minimum possible value of

b

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