For ab ≠0, if * is defined by a * b = \frac{a^2+b^2}{ab} then \frac{(1*2)*(2*1)}{(1*3)+(3*1)} =

TS ICET 23 May 2019 Shift 1 Paper

Question : 75 of 200

Marks: +1, -0

For ab ≠0, if * is defined by a * b =

{a^2+b^2}/{ab}

then

{(1*2)*(2*1)}/{(1*3)+(3*1)}

Solution:

(1^{*} 2)=\;{1^{2}+2^{2}}/{(1)(2)}=\;{5}/{2}

(2^{*} 1)=\;{2^{2}+1^{2}}/{(2)(1)}=\;{5}/{2}

(1^{*} 3)=\;{1^{2}+3^{2}}/{(1)(3)}=\;{10}/{3}

(3^{*} 1)=\;{3^{2}+1^{2}}/{(3)(1)}=\;{10}/{3}

\;{(1 * 2) *(2 * 1)}/{(1 * 3)+(3 * 1)}=\;{({5}/{2} * {5}/{2})}/{{10}/{3}+\;{10}/{3}}

(\;{5}/{2} * \;{5}/{2})=\;{({5}/{2})^{2}+({5}/{2})^{2}}/{(\;{5}/{2})(\;{5}/{2})}=\;{\;{25}/{4}+{25}/{4}}/{{25}/{4}}=2

=\;{({5}/{2} * {5}/{2})}/{{20}/{3}}=2 × \;{3}/{20}=\;{3}/{10}

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