Question

solve the quadratic equation by formula method.
$4 {z}^{2} + \frac{6}{ {z}^{2} } \: = 11$
Please it's urgent...​

Answer 1

Answer:

tex]4 {z}^{2} + \frac{6}{ {z}^{2} } \: = 11[/tex]

answer

Answer 2

Topic

Quadratic equations

Solution

$\sf{4 {z}^{2} + \dfrac{6}{ {z}^{2}} = 11}$

Let us assume z² as y

So substitute z² with y

$\sf{ \implies \: 4y +\dfrac{6}{y}=11}$

$\sf{ \implies4y +\dfrac{6}{y}-11=0}$

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Take L.CM

⠀️️️️️️

$\sf{ \implies \dfrac{4y²+6-11y}{y}=0}$

$\sf{ \implies4y²+6-11y}=0$

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Now solve the quadratic equation by formula method

$\mathtt { a= 4 , \: b = -11 , \: c= 6}$

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$\bold{D= b²-4ac}$

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$\sf{ \to \:D= (-11)²-4×4×6} \\ \\ \sf{ \to \:D= 121-96}$

$\sf{ \to \red{D = 25}}$

⠀️️️️️️

$\bold{x=\dfrac{-b-√D}{2a}\:\:or\: </p><p>\:\dfrac{-b+√D}{2a}}$

⠀️️️️️️

$\sf{ \implies \: y=\dfrac{-(-11)-√25}{2×4} \: \: or \: \: \dfrac{-(-11)+√25}{2×4}}$

$\sf{ \implies \: y = \dfrac{11-5}{8} \: \: or \: \: \dfrac{11+5}{8}} \\ \\ \sf{ \implies \: y= \dfrac{6}{8} \: \: or \: \: \dfrac{16}{8}}$

⠀️️️️️️

$\sf{ \implies \: y= \dfrac{3}{4} \: \: or \: \: 2}$

$\sf{ \implies \: z²= y = \dfrac{3}{4} \: \: or \: \: 2}$

⠀️️️️️️

$\sf{ \implies \: z =  ± \sqrt{ \frac{3}{4} } } \: \: or  ±\sqrt{2} \\ \\ \sf{ \implies \red{z = \frac{ \sqrt{3} }{2} , - \frac{ \sqrt{3} }{2} , \sqrt{2} , - \sqrt{2} }}$

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