If a- b- c- d are in H-P- then the value of 1a2 - 1d2 1b2 - 1c2 is

The correct option is D 3 1a, 1b, 1c, 1d are in A.P. and let these four terms be α 3β, α β, α + β, α + 3β L.H.S. = (α 3β)^2 (α + 3β ...

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Higher Order Derivatives

If a, b, c,...

Question

If $a, b, c, d$ are in H.P., then the value of $(\frac{1}{a^{2}} - \frac{1}{d^{2}}) (\frac{1}{b^{2}} - \frac{1}{c^{2}})$ is

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a, b, c

a^{2} = b^{2} + c^{2} - 2 b c \sqrt{1 - a^{2}}, b^{2} = c^{2} + a^{2} - 2 c a \sqrt{1 - b^{2}}, c^{2} = a^{2} + b^{2} - 2 a b \sqrt{1 - c^{2}}

a = c \sqrt{1 - b^{2}} + b \sqrt{1 - c^{2}}

a, b, c

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

a < b < c

a + b + c = \frac{3}{4}

a

(\frac{1}{b} + \frac{1}{c} - \frac{1}{a}) (\frac{1}{c} + \frac{1}{a} - \frac{1}{b})

a, b, c

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

a < b < c

a + b + c = \frac{3}{2}

a

a + b + c = 0

\frac{1}{b^{2} + c^{2} - a^{2}} + \frac{1}{c^{2} + a^{2} - b^{2}} + \frac{1}{a^{2} + b^{2} - c^{2}}

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