Question

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

Answer 1

Heya User,


--> ( 3x )² - ( 3x )( a² + b² + a² - b² ) + ( a⁴ - b⁴ ) = 0

=>  ( 3x )² - ( 3x )( a² + b² ) - ( 3x )( a² - b² ) + ( a⁴ - b⁴ ) = 0
=> ( 3x )( 3x - a² - b² ) - ( a² - b² )( 3x - a² - b² )
=> ( 3x - a² + b² )( 3x - a² - b² )  √√ Done ^_^

Further factorization :->
---> [ 3x - ( a + b )( a - b ) ][ 3x - [ a² + b² ]]

Answer 2

Answer:

9x^2-6b^2x-(a^4-b^4)

9x^2-6b^2x-a^4+b^4

By quadratic formula:

D=(-6b^2)^2-4×9×(-a^4+b^4)

D=36b^4+36a^4-36b^4

D=36a^4

Now,

X=-(-6b^2)+-√36a^4/2×9

X=6b^2+-6a^2/18

X=6b^2+6a^2/18

X=6(b^2+a^2)/18

X=b^2+a^2/3

X=6b^2-6a^2/18

X=6(b^2-a^2)/18

X=b^2-a^2/3

X=-(a^2-b^2)/3

So, the value of X=a^2+b^2/3,

X=-(a^2-b^2)/3

Hope it's help you