Question

solve for x :
$9 {x}^{2} - 6 {a}^{2} x + ( {a}^{4} - {b}^{4} ) = 0$
​

Answer 1

Step-by-step explanation:

$\huge{\bold☘}\mathfrak\pink{\bold{\underline{{ ℘ɧεŋσɱεŋศɭ}}}}{\bold☘}$

$\huge\tt\red{\bold{\underline{\underline{❥Question᎓}}}}$solve for x :

$9 {x}^{2} - 6 {a}^{2} x + ( {a}^{4} - {b}^{4} ) = 0$

$\huge\tt{\boxed{\overbrace{\underbrace{\blue{Answer</p><p> }}}}}$

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_ _ _ _ _ _ _ _ _ _ _ _ _ _ _✍️

$\bold{ GIVEN}$:$9 {x}^{2} - 6 {a}^{2} x + ( {a}^{4} - {b}^{4} ) = 0$

$⟹</p><p>9 {x}^{2} - 6 {a}^{2} x + ( {a}^{4} - {b}^{4} ) = 0$

$⟹</p><p>9 {x}^{2} - 6 {a}^{2} x + ( {a}^{2} + {b}^{2} )( {a}^{2} - {b}^{2} ) = 0$

$⟹</p><p>\bold{Here\:product \:of \:coefficient \:of \:x \:square \:and \:the \:constant \:term}$

$= 9( {a}^{2} + {b}^{2} )( {a}^{2} - {b}^{2} )$

$= (3 {a}^{2} + 3 {b}^{2} )(3 {a}^{2} - 3 {b}^{2} )$

$so \: that \: 3 {a}^{2} + 3 {b}^{2} + 3 {a}^{2} - 3 {b}^{2} = 6 {a}^{2}$

$⟹</p><p>\bold{∴ The\: given\: quadratic \:equation\: can\: be\: written\: as }$

$⟹</p><p>9 {x}^{2} - (3( {a}^{2} + {b}^{2} ) + 3( {a}^{2} - {b}^{2} ))x + ( {a}^{2} + {b}^{2} )( {a}^{2} - {b}^{2} ) = 0$

$⟹</p><p>9 {x}^{2} - 3x( {a}^{2} + {b}^{2} ) - 3x( {a}^{2} - {b}^{2} ) + ( {a}^{2} + {b}^{2} )( {a}^{2} - {b}^{2} ) = 0$

$⟹</p><p>3x(3x - {a}^{2} - {b}^{2} ) - ( {a}^{2} - {b}^{2} )(3x - {a}^{2} - {b}^{2} ) = 0$

$⟹</p><p>( 3x - {a}^{2} - {b}^{2} )(3x - {a}^{2} + {b}^{2} ) = 0$

$⟹</p><p>3x - {a}^{2} - {b}^{2} = 0$

$⟹</p><p>3x - {a}^{2} + {b}^{2} = 0$

$⟹</p><p>3x = {a}^{2} + {b}^{2}$

$⟹</p><p>3x = {a}^{2} - {b}^{2}$

$⟹</p><p>x = \frac{ {a}^{2} + {b}^{2} }{3}$

$⟹</p><p> = \frac{ {a}^{2} - {b}^{2} }{3}$

$\bold{∴The\: solution\: of \:given\: quadratic \:equation\: are:-}$

$\bold{\red{ \frac{ {a}^{2} + {b}^{2} }{3} \: and \: \frac{ {a}^{2} - {b}^{2} }{3} }}$

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нσρє ıт нєłρs yσυ

_____________________

тнαηkyσυ

Answer 2

Step-by-step explanation:

Step-by-step explanation:

\huge{\bold☘}\mathfrak\pink{\bold{\underline{{ ℘ɧεŋσɱεŋศɭ}}}}{\bold☘}☘

℘ɧεŋσɱεŋศɭ

☘

\huge\tt\red{\bold{\underline{\underline{❥Question᎓}}}}

❥Question᎓

solve for x :

9 {x}^{2} - 6 {a}^{2} x + ( {a}^{4} - {b}^{4} ) = 09x

2

−6a

2

x+(a

4

−b

4

)=0

\huge\tt{\boxed{\overbrace{\underbrace{\blue{Answer }}}}}

Answer

╔════════════════════════╗

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _✍️

\bold{ GIVEN}GIVEN :9 {x}^{2} - 6 {a}^{2} x + ( {a}^{4} - {b}^{4} ) = 09x

2

−6a

2

x+(a

4

−b

4

)=0

⟹ 9 {x}^{2} - 6 {a}^{2} x + ( {a}^{4} - {b}^{4} ) = 0⟹9x

2

−6a

2

x+(a

4

−b

4

)=0

⟹ 9 {x}^{2} - 6 {a}^{2} x + ( {a}^{2} + {b}^{2} )( {a}^{2} - {b}^{2} ) = 0⟹9x

2

−6a

2

x+(a

2

+b

2

)(a

2

−b

2

)=0

⟹ \bold{Here\:product \:of \:coefficient \:of \:x \:square \:and \:the \:constant \:term}⟹Hereproductofcoefficientofxsquareandtheconstantterm

= 9( {a}^{2} + {b}^{2} )( {a}^{2} - {b}^{2} )=9(a

2

+b

2

)(a

2

−b

2

)

= (3 {a}^{2} + 3 {b}^{2} )(3 {a}^{2} - 3 {b}^{2} )=(3a

2

+3b

2

)(3a

2

−3b

2

)

so \: that \: 3 {a}^{2} + 3 {b}^{2} + 3 {a}^{2} - 3 {b}^{2} = 6 {a}^{2}sothat3a

2

+3b

2

+3a

2

−3b

2

=6a

2

⟹ \bold{∴ The\: given\: quadratic \:equation\: can\: be\: written\: as }⟹∴Thegivenquadraticequationcanbewrittenas

⟹ 9 {x}^{2} - (3( {a}^{2} + {b}^{2} ) + 3( {a}^{2} - {b}^{2} ))x + ( {a}^{2} + {b}^{2} )( {a}^{2} - {b}^{2} ) = 0⟹9x

2

−(3(a

2

+b

2

)+3(a

2

−b

2

))x+(a

2

+b

2

)(a

2

−b

2

)=0

⟹ 9 {x}^{2} - 3x( {a}^{2} + {b}^{2} ) - 3x( {a}^{2} - {b}^{2} ) + ( {a}^{2} + {b}^{2} )( {a}^{2} - {b}^{2} ) = 0⟹9x

2

−3x(a

2

+b

2

)−3x(a

2

−b

2

)+(a

2

+b

2

)(a

2

−b

2

)=0

⟹ 3x(3x - {a}^{2} - {b}^{2} ) - ( {a}^{2} - {b}^{2} )(3x - {a}^{2} - {b}^{2} ) = 0⟹3x(3x−a

2

−b

2

)−(a

2

−b

2

)(3x−a

2

−b

2

)=0

⟹ ( 3x - {a}^{2} - {b}^{2} )(3x - {a}^{2} + {b}^{2} ) = 0⟹(3x−a

2

−b

2

)(3x−a

2

+b

2

)=0

⟹ 3x - {a}^{2} - {b}^{2} = 0⟹3x−a

2

−b

2

=0

⟹ 3x - {a}^{2} + {b}^{2} = 0⟹3x−a

2

+b

2

=0

⟹ 3x = {a}^{2} + {b}^{2}⟹3x=a

2

+b

2

⟹ 3x = {a}^{2} - {b}^{2}⟹3x=a

2

−b

2

⟹ x = \frac{ {a}^{2} + {b}^{2} }{3}⟹x=

3

a

2

+b

2

⟹ = \frac{ {a}^{2} - {b}^{2} }{3}⟹=

3

a

2

−b

2

\bold{∴The\: solution\: of \:given\: quadratic \:equation\: are:-}∴Thesolutionofgivenquadraticequationare:−

\bold{\red{ \frac{ {a}^{2} + {b}^{2} }{3} \: and \: \frac{ {a}^{2} - {b}^{2} }{3} }}

3

a

2

+b

2

and

3

a

2

−b

2

╚════════════════════════╝

нσρє ıт нєłρs yσυ

_____________________

тнαηkyσυ