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The value of 1/"x"^2+1/"y"^2, where x = 2 +sqrt3 and y =2-sqrt3 is - Mathematics

MCQ

The value of `1/"x"^2+1/"y"^2`, where x = `2 +sqrt3` and y `=2-sqrt3`, is

Options

  • 12

  • 16

  • 14

  • 10

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Solution

14

Explanation:

x = `2+sqrt3` ,  y =`2-sqrt3`

`1/"x"=1/(2+sqrt3)`   `1/"y"=1/(2-sqrt3)`

By Rationalizing

`1/"x"=1/((2+sqrt3))((2-sqrt3))/((2-sqrt3))1/"y"=((2+sqrt3))/((2-sqrt3)(2+sqrt3))`

`1/"x"=2-sqrt3`        `1/"y"=2sqrt3`

`1/"x"^2=(2-sqrt3)^2`   

`1/"y"^2=(2+sqrt3)^2`1/"x"^2+1/"y"^2=2^2+(sqrt3)^2-4sqrt3+2^2+(sqrt3)^2+4sqrt3`

`1/"x"^2+1/"y"^2=4+4+3+3+=14`

Concept: Number System (Entrance Exam)
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