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Sol v e :(x^2-4x+7)/(x^2-7x+12)lt=2/3dot...

`Sol v e :(x^2-4x+7)/(x^2-7x+12)lt=2/3dot`

Text Solution

Verified by Experts

`frac{3(x^2-4x+7)-2(x^2-7x+12)}{3(x^2-7x+12)}<=0`
`frac{x^2+2x-3}{x^2-7x+12}<=0`
`frac{(x-1)(x+3)}{(x-4)(x-3)}<=0`
`x in (-3, 1) cup (3, 4)`
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Knowledge Check

  • If (x^(2) - x - 1)^(x^(2) - 7x + 12) = 1 then

    A
    Positive integral solutions are `4`
    B
    Negative integral solutions are `2`
    C
    non positive integral solution are `2`
    D
    Total integral solutions are `6`

  • Let S is the region of points which satisfies y^(2)lt16x,x lt4 and (xy(x^(2)-3x+2))/(x^(2)-7x+12)gt0 . Its area is

    A
    `(8)/(3)`
    B
    `(64)/(3)`
    C
    `(32)/(3)`
    D
    none of these

  • What is the value of ((x ^(2) -x - 6)/(x ^(2) + x - 12)) + ((x ^(2) + 5x + 6)/(x ^(2) + 7x + 12)) ?

    A
    1
    B
    `((x- 3))/((x+ 3))`
    C
    `((x+ 4))/(( x - 3))`
    D
    `((x - 3))/( (x + 4))`

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