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Basic of Logarithms
easy
જો ${{{x^2}} \over {({x^2} + {a^2})\,({x^2} + {b^2})}} = k\left( {{{{a^2}} \over {{x^2} + {a^2}}} - {{{b^2}} \over {{x^2} + {b^2}}}} \right)$ તો $k =$
A
${a^2} - {b^2}$
B
${1 \over {a + b}}$
C
${1 \over {a - b}}$
D
${1 \over {{a^2} - {b^2}}}$
Solution
(d) ${x^2} = k\,\,[{a^2}({x^2} + {b^2}) – {b^2}({x^2} + {a^2})]$
$ \Rightarrow $${x^2} = k\,[({a^2} – {b^2}){x^2}] \Rightarrow 1 = k({a^2} – {b^2})$
$\therefore k = {1 \over {{a^2} – {b^2}}}$.
Standard 11
Mathematics