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Basic of Logarithms
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The rationalising factor of ${a^{1/3}} + {a^{ - 1/3}}$ is
A
${a^{1/3}} - {a^{ - 1/3}}$
B
${a^{2/3}} + {a^{ - 2/3}}$
C
${a^{2/3}} - {a^{ - 2/3}}$
D
${a^{2/3}} + {a^{ - 2/3}} - 1$
Solution
(d) Let$x = {a^{1/3}},y = {a^{ – 1/3}}$then $a = {x^3},{a^{ – 1}} = {y^3}$
${x^3} + {y^3} = (x + y)({x^2} – xy + {y^2})$
So, rationlising factor is $({x^2} – xy + {y^2})$. Put the value of $x$ and $y$.
Thus the required rationlising factor is ${a^{2/3}} + {a^{ – 2/3}} – 1$.
Standard 11
Mathematics
