Number of positive integral solution of the e | vedclass

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Question

$\begin{aligned} xyx &=90=2,3^{2}, 5^{1} \ 	ext { Let } x &=2^{ x _{1}} 3^{ y _{1}} 5^{ Z _{1}} \ y &=2^{ x _{1}} 3^{ y _{2}} 5^{ z _{2

Vedclass · Accepted Answer

$54$

Vedclass · Answer

$\begin{aligned} xyx &=90=2,3^{2}, 5^{1} \ 	ext { Let } x &=2^{ x _{1}} 3^{ y _{1}} 5^{ Z _{1}} \ y &=2^{ x _{1}} 3^{ y _{2}} 5^{ z _{2}} \ z &=2^{ x _{3}} 3^{ y _{3}} 5^{ z _{3}} \end{aligned}$

$x _{1}+ x _{2}+ x _{3}=1 ightarrow\left(\begin{array}{c}1+3-1 \ 3-1\end{array}ight)=\left(\begin{array}{l}3 \ 2\end{array}ight)=3$

$y _{1}+ y _{2}+ y _{3}=2 ightarrow\left(\begin{array}{c}2+3-1 \ 3-1\end{array}ight)=\left(\begin{array}{c}4 \ 2\end{array}ight)=6$

$z _{1}+ z _{2}+ z _{3}=1 ightarrow\left(\begin{array}{c}1+3-1 \ 3-1\end{array}ight)=\left(\begin{array}{l}3 \ 2\end{array}ight)=3$

$3,6,3=54 ways$

Number of positive integral solution of the equation $xyz = 90$ is equal to :-

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