Question

plz my elder brother ,sister,teacher solve my this hard question। but before making spam think १०० times ​

Answer 1

Answer:

6 ± √ 10

Step-by-step explanation:

Given :

( x - 1 ) / ( x - 2 ) + ( x - 3 ) / ( x - 4 ) = 2 ( 1 / 3 )

= > [ ( x - 1 ) ( x - 4 ) + ( x - 3 ) ( x - 2 ) ] / [ ( x - 2 ) ( x - 4 ) = 7 / 3

= >3  [ ( x - 1 ) ( x - 4 ) + ( x - 3 ) ( x - 2 ) ] = 7 [ ( x - 2 ) ( x - 4 )

= > 3 [ x² - 4 x - x + 4 + x² - 3 x - 2 x + 6 ] = 7 [ x² - 4 x - 2 x + 8 ]

= > 3 [ 2 x² - 10 x + 10 ] = 7 [ x² - 6 x + 8 ]

= > 6 x² - 30 x + 30 = 7 x² - 42 x + 56

= > x² - 12 x + 26 = 0

Using quadratic formula  :

i.e. x = ( - b ± √ ( b² - 4 a c ) ) / 2 a

= > x = ( - ( - 12 ) ± √ ( - 12 )² - 4 × 1 × 26 ) / 2 × 1

= > x = 12 ± √ ( 144 - 104 ) / 2

= > x = 12 ± √ 40 / 2

= > x =  2 ( 6 ± √ 10) / 2

= > x = 6 ± √ 10

Therefore , roots of equation is 6 ± √ 10.

Answer 2

Answer:

x = 6 ± √10

Step-by-step explanation:

Let,

      x - 2 = a.

  So,

     x - 1 = x - 2 + 1 = a + 1

     x - 3 = x - 2 - 1 =  a - 1

     x - 4 = x - 2 - 2 = a - 2

Therefore, now, given equation is :

⇒ ( a + 1 ) / a + ( a - 1 ) / ( a - 2 ) = 7 / 3           { 2 1/3 = ( 3(2) + 1 } / 3 =  7 / 3 }

Splitting the terms : write ( a + 1 ) / a as ( a / a ) + ( 1 / a )

                     And, ( a - 1 ) / ( a - 2 ) as ( a - 2 + 1  ) / ( a - 2 ) = [ ( a - 2 ) / ( a - 2 ) + 1 / ( a - 2 ) ]

⇒ [ ( a / a ) + ( 1 / a ) ] + [ ( a - 2 ) / ( a - 2 ) + 1 / ( a - 2 ) ]  = 7 / 3

⇒  [ 1 + ( 1 / a ) ] + [ 1 + 1 / ( a - 2 ) ] = 7 / 3

⇒ ( 1 / a ) + 1 / ( a - 2 ) + 2 = 7 / 3

⇒ [ a - 2 + a ] / a( a - 2 ) = 7 / 3 - 2

⇒  ( 2a - 2 ) / a( a - 2 ) = ( 7 - 6 ) / 3 = 1 / 3

⇒ 3( 2a - 2 ) = a( a - 2 )

⇒  6a - 6 = a^2 - 2a

⇒ a^2 - 8a + 6 = 0

Using Quadratic Formula :

⇒ a = [ - ( - 8 ) ± √{ 8^2 - 4( 6 ) } ] / 2

⇒ a = [ 8 ± √( 64 - 24  ) ] / 2

⇒ a = [ 8 ± √40 ] / 2

⇒ a = ( 8 + 2√10 ) / 2

⇒ a = 4 ± √10

⇒ x - 2 = 4 ± √10

⇒ x = 6 ± √10