If x, y are two positive real number and $${x^{\frac{1}{3}}} = {y^{\frac{1}{4}}},$$ then which of the following relations is true?
A. x3 = y4
B. x3 = y
C. x = y4
D. x20 = y15
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & {\text{ }}{x^{\frac{1}{3}}} = {y^{\frac{1}{4}}}, \cr & \Rightarrow {\text{LCM of 3, 4}} = 12{\text{ }} \cr & \therefore {\text{ }}{\left( {{x^{\frac{1}{3}}}} \right)^{12}} = {\left( {{y^{\frac{1}{4}}}} \right)^{12}} \cr & \Rightarrow {x^4} = {y^3} \cr & {\text{take power '5' on both sides}} \cr & \Rightarrow {\left( {{x^4}} \right)^5} = {\left( {{y^3}} \right)^5} \cr & \Rightarrow {x^{20}} = {y^{15}} \cr} $$Join The Discussion
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