સમીકરણ xyz = 2^5 × 3^2 × 5^2 ના પ્રકૃતિક ઉકેલ?

English

Gujarati

Hindi

4-2.Quadratic Equations and Inequations

normal

સમીકરણ $xyz = 2^5 \times 3^2 \times 5^2$ ના પ્રકૃતિક ઉકેલોની સંખ્યા ........ થાય

$756$

$520$

$720$

$120$

$xyz = {2^5} \times {3^2} \times {5^2}$

let $x = {2^{{a_1}}}{3^{{b_1}}}{5^{{c_1}}}$

$y = {2^{{a_2}}}{3^{{b_2}}}{5^{{c_2}}}$

$z = {2^{{a_3}}}{3^{{b_3}}}{5^{{c_3}}}$

then $xyz = {2^{{a_1} + {a_2} + {a_3}}}{3^{{b_1} + {b_2} + {b_3}}}{5^{{c_1} + {c_2} + {c_3}}}$

$ \Rightarrow {a_1} + {a_1} + {a_1} = 5$

${b_2} + {b_2} + {b_3} = 2$

${c_1} + {c_2} + {c_3} = 2$

Standard 11

Mathematics

hard

medium

(JEE MAIN-2021)

easy

hard

(JEE MAIN-2023)

hard