If * is defined by a * b = a^3+b^3-3ab for a , b ∊ R, then \frac{(1*2)*(1*2)}{(1*)*(1*1)} =

TS ICET 23 May 2019 Shift 1 Paper

Question : 73 of 200

Marks: +1, -0

If * is defined by a * b =

a^3+b^3-3ab

for a , b ∊ R, then

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

Solution:

(1 * 2)=1^{3}+2^{3}-3(1)(2)=3

(1 * 1)=1^{3}+1^{3}-3(1)(1)=-1

\;{(1 * 2) *(1 * 2)}/{(1 * 1) *(1 * 1)}=\;{3 * 3}/{(-1) *(-1)}

3^{*} 3=3^{3}+3^{3}-3(3)(3)=27

(-1)^{*}(-1)=(-1)^{3}+(-1)^{3}-3(-1)(-1)

=-1-1-3=-5

\;{3 * 3}/{(-1) *(-1)}=\;{-27}/{5}

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