Question

❤❤Aloha Friends ❤❤ Urgent questions !!

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✴ 4x^2 + 20 x + 9 = 0

===> Solve this by using Method of Completion of Square

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✴ 3x^2 + 23x + 14 = 0

=====> Solve by using Formula Method
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✴ 1/a + 1/b + 1/x = 1/a + b+ x

=====> Solve by Factorization
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Brainly Team

Answer 1

▶ 4x² + 20x + 9 = 0



Divide by 4 on both sides ,



= > ( 4x² / 4 ) + ( 20x / 4 ) + ( 9 / 4 ) = 0


= > x² + 5x = - 9 / 4



Add ( 5 / 2 )² on both sides ,



= > x² + 5x + ( 5 / 2 )² = - 9 / 4 + ( 5 / 2 )²


$= > (x + \frac{5}{2}) {}^{2} = \frac{ - 9 + 25}{4} \\ \\ \\ \\ = > {(x + \frac{5}{2} )}^{2} = \frac{16}{4} \\ \\ \\ \\ = > {(x + \frac{5}{2} )}^{2} = 4 \\ \\ \\ \\ = > x + \frac{5}{2} = \pm2$



$= \: > x =[ \: \: 2 - \frac{5}{2 } \: \: \: ] \: \: \: or \: \: \: [ \: \: - 2 - \frac{5}{2} \: \: ] \\ \\ \\ \\ = \: >x = \: \: - \frac{1}{2} \: \: \: \: \: \: or \: \: \: \: \: \: \: \: - \frac{ 9}{2} \: \: \:$







▶ 3x² + 23x + 14 = 0



On comparing the given equation with { ax² + bx + c = 0 } , we get

a = 3
b = 23
c = 14




✖ Discriminant = b² - 4ac

= > ( 23 )² - 4( 3 × 14 )


= > 529 - 168


= > 361





Applying Shri Dharacharya's Formula , { Formula Method } ,


$x = \frac{ - b \pm \sqrt{discriminant} }{2a}$



Putting values,


$= > x = \frac{ - ( \: 23 \: ) \pm \sqrt{361} }{2(3)} \\ \\ \\ \\ = > \boxed{x = \frac{ - 23 + 19}{6} } \: \: \: \: \: or \: \: \: \: \: \boxed{ x = \frac{ - 23 - 19}{6} } \\ \\ \\ \\ = > \boxed{x = - \frac{42}{6} } \: \: \: \: \: or \: \: \: \: \: \boxed{x = - \frac{4}{6} } \\ \\ \\ \\ = > \boxed{ x = - 7 \: \: \: \: or \: \: \: \: - \frac{2}{3} }$






▶ 1 / a + 1 / b + 1 / x = 1 / { a + b + x }



$= > \frac{1}{a} + \frac{1}{b} = \frac{1}{a + b + x} - \frac{1}{x} \\ \\ \\ \\ = > \frac{b + a}{ab} = \frac{ \cancel{x }- a - b - \cancel{x}}{(a + b + x)x}$
$= > \frac{a + b}{ab} = \frac{ - a - b}{(a + b + x)x} \\ \\ \\ \\ = > \frac{ \cancel{(a + b)}}{ab} = \frac{ - \cancel{ (a + b)}}{(a + b + x)x} \\ \\ \\ \\ = > \frac{1}{ab} = \frac{ - 1}{(a + b + x)x}$




= > ax + bx + x² = - ab


= > x² + ax + bx + ab = 0


= > x( x + a ) + b( x + a ) = 0


= > ( x + a ) ( x + b ) = 0




$\: \: \: \: \: \: \: \: \: \:By \: \: Zero \: \: Product \: \: Rule , \\ \\ \\ \\ \boxed{x = - a \: \: \: \: \: o r \: \: \: \: x = - b}$

Answer 2

Heya mate.....refer attachment.....hope it helps u.....@skb♥️