If 7/{3^{2/3}-12^{1/3}+4^{2/3}}= a\sqrt^3{3} + b\sqrt^3{4} + c\sqrt^3{6} , then find a + b + c

SSC CGL Model Paper 5

Question : 55 of 100

Marks: +1, -0

7/{3^{2/3}-12^{1/3}+4^{2/3}}= a√^3{3} + b√^3{4} + c√^3{6}

, then find

a + b + c

Solution:

7/({3^{2/3}-12^{1/3}+4^{2/3}})×(3^{1/3}+4^{1/3})/(3^{1/3}+4^{1/3})

={7(3^{1/3}+4^{1/3})}/{(3^{1/3}+4^{1/3})\{(3^{1/3})^2-(3^{1/3}.4^{1/3})+(4^{1/3})^2\}}

={7(3^{1/3}+4^{1/3})}/{(3^{1/3})^3+(4^{1/3})^3

(∵ a^3 + b^3 = (a + b) (a^2 - ab +b^2)

={7(3^{1/3}+4^{1/3})}/{3+4}=3^{1/3}+4^{1/3}

⇒

a√^3{3} + b√^3{4} + c√^3{6}=√^3{3}+√^3{4}

Now, com paring coefficients.

a = 1 , b = 1 , c = 0

⇒

a + b + c = 1 + 1 + 0 = 2

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