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If x=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))...

If `x=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))` and `y=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2))` , find `x^2+y^2`

Text Solution

Verified by Experts

`x=(sqrt3+sqrt2)/(sqrt3-sqrt2)`
After rationalizing
`x=(sqrt3+sqrt2)/(sqrt3-sqrt2)*(sqrt3+sqrt2)/(sqrt3+sqrt2)`
`x=(sqrt3+sqrt2)^2/(3-2)=3+2+2sqrt6`
`x=5+2sqrt6`
Similarly,
`y=5-2sqrt6`
`x^2+y^2=(5+2sqrt6)^2+(5-2sqrt6)^2`
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Knowledge Check

  • If x=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) and y=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) find the value of x^(3)+y^(3)

    A
    `807`
    B
    `907`
    C
    `970`
    D
    `870`

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    A
    1030
    B
    970
    C
    990
    D
    99

  • If x = ( sqrt( 3) + sqrt(2))/( sqrt(3) - sqrt(2)) and y = ( sqrt(3) - sqrt(2))/( sqrt(3) + sqrt(2)) then the value of ( x^(2) + 6 xy + y^(2))/( x^(2) - 6xy + y^(2)) is

    A
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