Complex Numbers And Quadratic Equations question 722
Question: If $ {x^{2/3}}-7{x^{1/3}}+10=0, $ then $ x= $ [BIT Ranchi 1992]
Options:
A) {125}
B) {8}
C) $ \varphi $
D) {125, 8}
Show Answer
Answer:
Correct Answer: D
Solution:
Given that $ {x^{2/3}}-7{x^{1/3}}+10=0 $ . Given equation can be written as $ {{({x^{1/3}})}^{2}}-7({x^{1/3}})+10=0 $ Let $ a={x^{1/3}} $ , then it reduces to the equation $ a^{2}-7a+10=0\Rightarrow (a-5)(a-2)=0\Rightarrow a=5,2 $ Putting these values, we have $ a^{3}=x\Rightarrow x=125 $ and 8.
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