Here it is:
If ( x + y ) ² = 100 and ( x - y ) ² = 16, what is the value of xy?
Please write out a step-by-step explanation with your answer so I can understand how you got there. 10 points to the best answer and major props from me.
If ( x + y ) ² = 100 and ( x - y ) ² = 16, what is the value of xy?
Please write out a step-by-step explanation with your answer so I can understand how you got there. 10 points to the best answer and major props from me.
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Ok, the value of x is 7 and y is 3. If you plug it in, (7+3)= 10. 10^2 is 100. Then (7-3)= 4. 4^2 is sixteen. Basically the easiest way is to find the square root of 100 (10) and plug in numbers that equal to 10 until they work in both equations.
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1) (X + Y)^2 = 100
2) (X + Y) ( X + Y) = 100
3) X^2 + 2XY + Y^2 = 100
1) (X-Y)^2 = 16
2) (X-Y)(X-Y) = 16
3) X^2 - 2XY + Y^2= 16
Add these two: X^2 + 2XY + Y^2 = 100
X^2 - 2XY + Y^2= 16
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2X^2 + 2Y^2 = 116
Divide by 2:
X^2 + Y^2 = 58
Substitute that into first equation:
58 + 2XY = 100
Divide by 2:
29+XY=100
Solve:
XY= 71
2) (X + Y) ( X + Y) = 100
3) X^2 + 2XY + Y^2 = 100
1) (X-Y)^2 = 16
2) (X-Y)(X-Y) = 16
3) X^2 - 2XY + Y^2= 16
Add these two: X^2 + 2XY + Y^2 = 100
X^2 - 2XY + Y^2= 16
___________________
2X^2 + 2Y^2 = 116
Divide by 2:
X^2 + Y^2 = 58
Substitute that into first equation:
58 + 2XY = 100
Divide by 2:
29+XY=100
Solve:
XY= 71
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... ( x + y )² = 100 ... and ... ( x - y )² = 16
∴ x² + y² + 2xy = 100 ... (1)
... x² + y² - 2xy = 16 ...... (2)
∴ EQ(1) - EQ(2) gives :
... 2xy - ( -2xy ) = 100 - 16
∴ 4xy = 84
∴ xy = 21 ............ Thats ur answer!
∴ x² + y² + 2xy = 100 ... (1)
... x² + y² - 2xy = 16 ...... (2)
∴ EQ(1) - EQ(2) gives :
... 2xy - ( -2xy ) = 100 - 16
∴ 4xy = 84
∴ xy = 21 ............ Thats ur answer!
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x+y=10, x-y=4. x=4+y, plug it into the other equation you get 4+y+y=10, 2y is 6. y equals 3. x minus 3 is 7, x equals 7.