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