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        find no of positive integral solution of x1x2x3=10800
2 years ago

moumi roy
91 Points
							can you make the question a bit clear i cant understand its meanig.please clear it can you make the question a bit clear i cant understand its meanig.please clear it

2 years ago
jagdish singh singh
173 Points
							$\hspace{-0.70 cm}Given x_{1}\cdot x_{2}\cdot x_{3} = 10800 = 2^4 \cdot 3^3 \cdot 5^2. Let x_{1} = 2^{a_{1}}\cdot 3^{b_{1}}\cdot 5^{c_{1}}\\\\ and x_{2} = 2^{a_{1}}\cdot 3^{b_{2}}\cdot 5^{c_{2}} and x_{3} = 2^{a_{3}}\cdot 3^{b_{3}}\cdot 5^{c_{3}} \\\\ So 2^{a_{1}+a_{2}+a_{3}}\cdot 3^{b_{1}+b_{2}+b_{3}}\cdot 5^{c_{1}+c_{2}+c_{3}} = 2^4 \cdot 3^3 \cdot 5^2\\\\ So a_{1}+a_{2}+a_{3}=4 and b_{1}+b_{2}+b_{3}=3 and c_{1}+c_{2}+c_{3} = 2\\\\ where a_{i}\in \{0,1,2,3,4\} and b_{i}\in \{0,1,2,3\} and c_{i}\in \{0,1,2\}\\\\$ $\hspace{-0.70 cm}So for calculation of all non negative integer ordered triplets of \\\\ a_{1}+a_{2}+a_{3}=4 . put a_{1}=0 get 5 ordered pair of (a_{2},a_{3}) \\\\ Similarly put a_{2}=0 get 3 ordered pair of (a_{2},a_{3}).\\\\ So Total 5+4+3+2+1 = 15\\\\ Similarly for b_{1}+b_{2}+b_{3}=3 we get 4+3+2+1=10\\\\ Similarly for c_{1}+c_{2}+c_{3} = 2 we get 3+2+1=6\\\\$ $\hspace{-0.70 cm} So we get total triplets  = 15 \times 10 \times 6 = 900$

2 years ago
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