Question

let f(x) =x^2+3x+4/x^2+5x+4 then solve inequality

Answer 1

Answer:

let f(x) =x^2+3x+4/x^2+5x+4 then solve inequality

Step-by-step explanation:

let f(x) =x^2+3x+4/x^2+5x+4 then solve a

Answer 2

Answer:The solution of inequality is that the roots are 7 and -9 respectively

Step-by-step explanation:

Given:We have given f(x) $= \frac{x^2+3x+4}{x^2+5x+4}$

To find:We have to find the inequality.

Explanation:

Step 1: Let f(x) $=\frac{x^2+3x+4}{x^2+5x+4} =$ $\beta$

⇒                   $x^{2} + 3x + 4$ $=$  $\beta$($x^2+5x+4$)

⇒                    $x^{2} + 3x + 4$ $=$ $x^{2}$ γ$+$ $5x$γ $+$ 4γ

⇒  $x^{2}$ $\beta$$+$ $5x$$\beta$ $+$ 4$\beta$ $-$ ( $x^{2} + 3x + 4$ ) $=$ $0$

⇒     $x^{2}$ $\beta$$+$ $5x$$\beta$ $+$ 4$\beta$  $-x^{2} -3x -4 = 0$  

⇒              $x^{2}$( $\beta$$-1$)$+x$($5$$\beta$$-3$)$+$($4$$\beta$$-4$) $= 0$

Step 2:We know that for 'x' to be real,

                    $D$≥$0$

Where $D=b^{2} -4ac$

Step 3:On solving we get,

⇒             $(5\beta -3)^{2} -4(\beta -1)(4\beta -4)= 0$

⇒   $(5\beta )^{2} -2(5\beta )(3)+(3)^{2} -4(4\beta ^{2} -4\beta -4\beta +4)= 0$

⇒          $25\beta ^{2} -30\beta +9-4(4\beta ^{2} -8\beta +4)= 0$

⇒         $25\beta ^{2} -30\beta+9-16\beta ^{2}+32\beta -16= 0$

⇒         $25\beta ^{2} -16\beta ^{2} -30\beta +32\beta +9-16= 0$

⇒                                          $9\beta ^{2} +2\beta -7= 0$

Step 4:Since 'D' for the above quadratic equation is positive.So roots of quadratic equation can be given by,

                 $x_{+} =\frac{-b+\sqrt{b^{2}-4ac } }{2}$ and $x_{-} =\frac{-b-\sqrt{b^{2}-4ac } }{2}$

Step 5:on solving $x_{+}$ and $x_{-}$ we get,

       $x_{+} =\frac{-(2)+\sqrt{2^{2}-4(9)(-7) } }{2}$

       $x_{+}= \frac{-2+\sqrt{4+252} }{2}$

       $x_{+} =\frac{-2+\sqrt{256} }{2}$

       $x_{+}=\frac{-2+(16)}{2}$

       $x_{+}=\frac{14}{2}$

       $x_{+}=7$

and

$x_{-} =\frac{-(2)-\sqrt{2^{2}-4(9)(-7) } }{2}$

$x_{-} =\frac{-(2)-\sqrt{2^{2}-4(9)(-7) } }{2}$

$x_{-}= \frac{-2-\sqrt{4+252} }{2}$

$x_{-} =\frac{-2-\sqrt{256} }{2}$

$x_{-}=\frac{-2-(16)}{2}$

$x_{-}=\frac{-18}{2}$

$x_{-}=-9$

Hence, the roots of above quadratic equation are 7 and -9 respectively.

∴∈(7,-9).

#SPJ2

Solve equation 7x-5/3x-5=9​

https://brainly.in/question/28565124

solve the inequality .

4x(x²-1)(x+3)²(x+2)>= 0

https://brainly.in/question/41883324