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If y is real, then the value of the expression \frac{y^{2}+14y+9}{y^{2}+2y+3} lies between 

  • Option 1)

    -3 and 3

  • Option 2)

    -4 and 5

  • Option 3)

    -4 and 4

  • Option 4)

    -5 and 4

 

Answers (1)

best_answer

As we learnt in 

Range -

The range of the relation R is the set of all second elements of the ordered pairs in a relation R.

- wherein

eg. R={(a,b),(c,d)}. Then Range is {b,d}

 

 x=\frac{y^{2}+14y+9}{y^{2}+2y+3}\\*\\*y^{2}\left ( x-1 \right )+2y\left ( x-7+3\left ( x-3 \right ) \right )=0\\*\\*D=4\left ( x-7 \right )^{2}-4\times 3\left ( x-1 \right )\left ( x-3 \right )> 0\\*\\*\left ( x^{2}+49-14x \right )-3\left ( x^{2}-4x+3 \right )> 0\\*\\*-2x^{2}-2x+40> 0\\*\\*x^{2} +x-20< 0\\*\\*x^{2} +5x-4x-20< 0\\*\\*\left (x-4 \right )\left ( x+5 \right )< 0\\*\\*x\in \left ( -5,4 \right )


Option 1)

-3 and 3

Incorrect

Option 2)

-4 and 5

Incorrect

Option 3)

-4 and 4

Incorrect

Option 4)

-5 and 4

Correct

Posted by

Aadil

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