Match the following- begin array -c- c - hline1- Weight of a a bangle-a- Litrelllhline2-Water in a a can-b- Kilogramlllhline3-Bag of wheat-c- Milligramlllhline lendarray A- 1- c2- a3-bB- 1- b2 - c 3-a1-bC- 1- b2- a3- cD- 1- a2-b3 - c

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Standardising Length Measurement

Match the fol...

Question

Match the following:
$\begin{matrix} 1. W e i g h t o f a b a n g l e & a . L i t r e 2. W a t e r i n a c a n & b . K i l o g r a m 3. B a g o f w h e a t & c . M i l l i g r a m \end{matrix}$

1 - c
2 - a
3 - b

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1 - b
2 - c
3 - a

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1 - b
2 - a
3 - c

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1 - a
2 - b
3 - c

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a + b + c = 1; a^{2} + b^{2} + c^{2} = 2; a^{3} + b^{3} + c^{3} = 3

If a, b, c are in G.P., prove that:

(i) $a (b^{2} + c^{2}) = c (a^{2} + b^{2})$

(ii) $a^{2} b^{2} c^{2} (\frac{1}{a^{3}} + \frac{1}{b^{3}} + \frac{1}{c^{3}}) = a^{3} + b^{3} + c^{3}$

(iii) $\frac{(a + b + c)^{2}}{a^{2} + b^{2} + c^{2}} = \frac{a + b + c}{a - b + c}$

(iv) $\frac{1}{a^{2} - b^{2}} + \frac{1}{b^{2}} = \frac{1}{b^{2} - c^{2}}$

(v) $(a + 2 b + 2 c) (a - 2 b + 2 c) = a^{2} + 4 c^{2}$ .

a^{3} + b^{3} + c^{3} - 3 a b c

a^{3} + 8 b^{3} + c^{3} - 6 a b c

a^{3} + b^{3} + c^{3} - 3 a b c = \frac{1}{2} (a + b + c) [{(a - b)}^{2} + {(b - c)}^{2} + {(c - a)}^{2}]

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