please answer this question
Answers
Answer:
x = 14 / 15 , y = 1 / 5
Step-by-step explanation:
Given---->
( 3x - 2iy ) ( 2 + i )² = 10 ( 1 + i )
To find ---> Value of x and y.
Solution---> We know that ,
i = √-1
Squaring both sides we get,
=> i² = ( - √1 )²
=> i² = -1
ATQ,
( 3x - 2iy ) ( 2 + i )² = 10 ( 1 + i )
We have an identity as follows,
( a + b )² = a² + 2ab + b² , we get,
=> ( 3x - 2iy ) { ( 2 )² + ( i )² + 2 ( 2 ) ( i ) } = 10 ( 1 + i )
=> ( 3x - 2iy ) ( 4 + i² + 4i ) = 10 + 10 i
Putting i² = -1 , we get,
=> ( 3x - 2iy ) ( 4 - 1 + 4i ) = 10 + 10 i
=> ( 3x - 2iy ) ( 3 + 4i ) = 10 + 10 i
=> 9x + 12ix - 6iy - 8 i² y = 10 + 10 i
Putting i² = -1 , we get,
=> 9x + 12ix - 6iy - 8 ( -1 ) y = 10 + 10i
=> 9x + i ( 12x - 6y ) + 8y = 10 + 10i
=> ( 9x + 8y ) + i ( 12x - 6y ) = 10 + 10i
Comparing real and imaginary part , we get,
9x + 8y = 10 ..................................( 1 )
12x - 6y = 10 ................................( 2 )
Multiplying equation ( 1 ) by 6 and equation ( 2 ) by 8 and then adding we get,
6 ( 9x + 8y ) + 8 ( 12x - 6y ) = 10 × 6 + 10 × 8
=> 54x + 48y + 96x - 48y = 60 + 80
=> 150 x = 140
=> x = 140 / 150
=> x = 14 / 15
putting x = 14 / 15 in equation ( 1 ) , we get,
9x + 8y = 10
=> 9 ( 14 / 15 ) + 8y = 10
=> 42 / 5 + 8y = 10
=> 8 y = 10 - 42/5
=> 8y = ( 50 - 42 ) / 5
=> 8y = 8 / 5
=> y = 1 / 5
#Answerwithquality
#BAL
Answer:
Step-by-step explanation:
Given---->
( 3x - 2iy ) ( 2 + i )² = 10 ( 1 + i )
To find ---> Value of x and y.
Solution---> We know that ,
i = √-1
Squaring both sides we get,
=> i² = ( - √1 )²
=> i² = -1
ATQ,
( 3x - 2iy ) ( 2 + i )² = 10 ( 1 + i )
We have an identity as follows,
( a + b )² = a² + 2ab + b² , we get,
=> ( 3x - 2iy ) { ( 2 )² + ( i )² + 2 ( 2 ) ( i ) } = 10 ( 1 + i )
=> ( 3x - 2iy ) ( 4 + i² + 4i ) = 10 + 10 i
Putting i² = -1 , we get,
=> ( 3x - 2iy ) ( 4 - 1 + 4i ) = 10 + 10 i
=> ( 3x - 2iy ) ( 3 + 4i ) = 10 + 10 i
=> 9x + 12ix - 6iy - 8 i² y = 10 + 10 i
Putting i² = -1 , we get,
=> 9x + 12ix - 6iy - 8 ( -1 ) y = 10 + 10i
=> 9x + i ( 12x - 6y ) + 8y = 10 + 10i
=> ( 9x + 8y ) + i ( 12x - 6y ) = 10 + 10i
Comparing real and imaginary part , we get,
9x + 8y = 10 ..................................( 1 )
12x - 6y = 10 ................................( 2 )
Multiplying equation ( 1 ) by 6 and equation ( 2 ) by 8 and then adding we get,
6 ( 9x + 8y ) + 8 ( 12x - 6y ) = 10 × 6 + 10 × 8
=> 54x + 48y + 96x - 48y = 60 + 80
=> 150 x = 140
=> x = 140 / 150
=> x = 14 / 15
putting x = 14 / 15 in equation ( 1 ) , we get,
9x + 8y = 10
=> 9 ( 14 / 15 ) + 8y = 10
=> 42 / 5 + 8y = 10
=> 8 y = 10 - 42/5
=> 8y = ( 50 - 42 ) / 5
=> 8y = 8 / 5
=> y = 1 / 5