How do I factorise 12x² - 7xy - 12y²?
回答 (6)
2009-07-16 10:12 am
✔ 最佳答案
12x^2 - 7xy - 12y^2= 12x^2 + 9xy - 16xy - 12y^2
= (12x^2 + 9xy) - (16xy + 12y^2)
= 3x(4x + 3y) - 4y(4x + 3y)
= (4x + 3y)(3x - 4y)
2009-07-16 6:54 pm
12x² - 7xy - 12y² = 0
x² - 7/12xy = y²
x² - 7/24xy = y² + (- 7/24y)²
x² - 7/24xy = 576/576y² + 49/576y²
(x - 7/24y)² = 625/576y²
x - 7/24y = ± 25/24y
= x - 7/24y - 25/24y, = x - 32/24y, = x - 4/3y, = 3x - 4y
= x - 7/24y + 25/24y, = x + 18/24y, = x + 3/4y, = 4x + 3y
Answer: (3x - 4y)(4x + 3y)
x² - 7/12xy = y²
x² - 7/24xy = y² + (- 7/24y)²
x² - 7/24xy = 576/576y² + 49/576y²
(x - 7/24y)² = 625/576y²
x - 7/24y = ± 25/24y
= x - 7/24y - 25/24y, = x - 32/24y, = x - 4/3y, = 3x - 4y
= x - 7/24y + 25/24y, = x + 18/24y, = x + 3/4y, = 4x + 3y
Answer: (3x - 4y)(4x + 3y)
2009-07-16 6:57 pm
Let a=12
b=-7y
c=-12y²
Using the quadratic formula:
x= [-b+/-(b²-4ac)^(1/2)]/(2a)
x= [7y+/-[49y²-4(12)(-12y²)]^(1/2)]/(2*12)
x=[7y+/-(49y²+576y²)^(1/2)]/24
x=[7y+/-(625y²)^(1/2)]/24
x=[7y+/-25y]/24
x=(7y+25y)/24= 32y/24= 4y/3 or x =(7y-25y)/24= -18y/24 = -3y/4
These are the values of x when 12x² - 7xy - 12y² is set to equal zero.
x=4y/3 and x=-3y/4 are roots.
3x=4y and 4x=-3y
3x-4y =0 and 4x+3y=0
thus (3x-4y) and (4x+3y) are factors:
12x² - 7xy - 12y² = (3x-4y)(4x+3y)
b=-7y
c=-12y²
Using the quadratic formula:
x= [-b+/-(b²-4ac)^(1/2)]/(2a)
x= [7y+/-[49y²-4(12)(-12y²)]^(1/2)]/(2*12)
x=[7y+/-(49y²+576y²)^(1/2)]/24
x=[7y+/-(625y²)^(1/2)]/24
x=[7y+/-25y]/24
x=(7y+25y)/24= 32y/24= 4y/3 or x =(7y-25y)/24= -18y/24 = -3y/4
These are the values of x when 12x² - 7xy - 12y² is set to equal zero.
x=4y/3 and x=-3y/4 are roots.
3x=4y and 4x=-3y
3x-4y =0 and 4x+3y=0
thus (3x-4y) and (4x+3y) are factors:
12x² - 7xy - 12y² = (3x-4y)(4x+3y)
2009-07-16 5:07 pm
(3x-4y) (4x+3y)
2009-07-16 5:04 pm
(3x-4y)(4x+3y)
= 3x*4x +3x*3y -4y*4x -4y*3y
= 12x² + 9xy - 16xy -12y²
= 12x² -7xy -12y²
QED
= 3x*4x +3x*3y -4y*4x -4y*3y
= 12x² + 9xy - 16xy -12y²
= 12x² -7xy -12y²
QED
2009-07-16 5:11 pm
12x² - 7xy - 12y²
=(4x+3y)(3x-4y) answer//
=(4x+3y)(3x-4y) answer//
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