root 3 x - root 2 Y = root 3 ,root 5 x + root 3 Y = root 2 solve by elimination method
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Hi ,
√3x - √2y = √3 ---( 1 )
√5x + √3y = √2 ---( 2 )
multiply equation ( 1 ) with √3 and equation
( 2 ) with √2 , we get ,
3x - √6y = 3 --( 3 )
√10x + √6y = 2 --( 4 )
add ( 3 ) and ( 4 ) , we get
3x + √10 x = 5
x ( 3 + √ 10 ) = 5
x = 5/( 3 + √10 )
x = [ 5( √10 - 3 ) ]/( √10 + 3 )( √10 - 3 )]
x = 5( √10 - 3 )/ [ ( √10 )² - ( 3 )² ]
x = 5( √10 - 3 )/ ( 10 - 9 )
x = 5√10 - 15
put x value in equation ( 2 ) , we get ,
√5 ( 5√10 - 15 ) + √3y = √2
25√2 - 15√5 + √3y = √2
√3y = √2 - 25√2 + 15√5
y = ( 15√5 - 24√2 )/√3
y = [ 3( 5√5 - 8√2 ) ]/( √3 )
y = [ √3 × √3 ( 5√5 - 8√2 )]/( √3 )
y = [ √3 ( 5√5 - 8√2 ) ]
y = 5√15 - 8√6
I hope this helps you.
: )
√3x - √2y = √3 ---( 1 )
√5x + √3y = √2 ---( 2 )
multiply equation ( 1 ) with √3 and equation
( 2 ) with √2 , we get ,
3x - √6y = 3 --( 3 )
√10x + √6y = 2 --( 4 )
add ( 3 ) and ( 4 ) , we get
3x + √10 x = 5
x ( 3 + √ 10 ) = 5
x = 5/( 3 + √10 )
x = [ 5( √10 - 3 ) ]/( √10 + 3 )( √10 - 3 )]
x = 5( √10 - 3 )/ [ ( √10 )² - ( 3 )² ]
x = 5( √10 - 3 )/ ( 10 - 9 )
x = 5√10 - 15
put x value in equation ( 2 ) , we get ,
√5 ( 5√10 - 15 ) + √3y = √2
25√2 - 15√5 + √3y = √2
√3y = √2 - 25√2 + 15√5
y = ( 15√5 - 24√2 )/√3
y = [ 3( 5√5 - 8√2 ) ]/( √3 )
y = [ √3 × √3 ( 5√5 - 8√2 )]/( √3 )
y = [ √3 ( 5√5 - 8√2 ) ]
y = 5√15 - 8√6
I hope this helps you.
: )
kushaldesai1:
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