SATHEE: Quantitative Aptitude Ques 2029

Quantitative Aptitude Ques 2029

Question: Directions: In the following questions, two equations numbered I and II are given. You have to solve both the equations and give answer [IBPS RRB (Office Assistant) 2012]

I. $ 2x^{2}-(4+\sqrt{13}),x+2\sqrt{13}=0 $ II. $ 10y^{2}-(18+5\sqrt{13})y+9\sqrt{13}=0 $

Options:

A) If $ x>y $

B) If $ x\ge y $

C) If $ x<y $

D) If $ x\le y $

E) If $ x=y $ or relationship cannot be established

Show Answer

Answer:

Correct Answer: A

Solution:

I. $ 2x^{2}-4x-\sqrt{13}x+2\sqrt{13}=0 $

$ \Rightarrow $ $ 2x(x-2)-\sqrt{13}(x-2)=0 $

$ \Rightarrow $ $ (x-2)(2x-\sqrt{13})=0 $

$ \therefore $ $ x=2, $ $ \frac{\sqrt{13}}{2} $ II. $ 10y^{2}-(18y)-5\sqrt{13}y+9\sqrt{13}=0 $

$ \Rightarrow $ $ 2y(5y-9)-\sqrt{13}(5y-9)=0 $

$ \Rightarrow $ $ (5y-9)(2y-\sqrt{13})=0 $

$ \therefore $ $ y=\frac{9}{5}, $ $ y=\frac{\sqrt{3}}{2} $ Hence, $ x\ge y $

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