JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

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Analyzing +4 | -1

x_1, x_2, x_3

and

x_4

are four positive real numbers such that

x_1+\frac{1}{x_2}=4, x_2+\frac{1}{x_3}=1

x_3+\frac{1}{x_4}=4

and

x_4+\frac{1}{x_1}=1

, then

View answer and explanation

Correct option: A

x_1=x_3

and

x_2=x_4

Option A (

x_1=x_3

and

x_2=x_4

) is correct because by applying AM-GM inequality and the given equations, it can be shown that

x_1 = x_3 = 2

and

x_2 = x_4 = 1/2

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