please answer this question
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2 answers · Mathematics
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The definition of a function is explained in 9th grade algebra. A question of this type is encountered at a level much higher than that. You should draw your own conclusions from those two facts.
Let's analyze the phrases in the question:
The phrase; "homogeneous function of second degree in x and y" means that you have a function:
f(x, y)
and in the function there are two terms, one containing x and the other containing y where and both are raised to the second power.
The phrase; "(2x - y) as a factor" gives us the following information.
f(x, y) =(2x - y){some other factor(s)}
The phrase; "vanishing if x = -1 and y = 1" means that (x + y) must be one of the other factors. Start with:
(x + y)
substitute -1 for x and 1 for y:
-1 + 1 = 0
This factor will be zero, thereby, forcing the entire function to vanish (become zero).
Recapping what we know:
f(x, y) = (2x - y)(x + y){maybe some other factors}
Let's check the value of just the two factors when x = y = 1
f(1, 1) = (2{1} - {1})({1} + {1})
f(1, 1)= (2 - 1)(1 + 1)
f(1, 1) = (1)(2)
f(1, 1) = 2
This works so there are no other factors:
f(x, y) = (2x - y)(x + y)
Use the F.O.I.L. method to multiply the factors:
f(x, y) = 2x² + 2xy - xy - y²
Combine like terms:
f(x, y) = 2x² + xy - y²
Best Answer
The definition of a function is explained in 9th grade algebra. A question of this type is encountered at a level much higher than that. You should draw your own conclusions from those two facts.
Let's analyze the phrases in the question:
The phrase; "homogeneous function of second degree in x and y" means that you have a function:
f(x, y)
and in the function there are two terms, one containing x and the other containing y where and both are raised to the second power.
The phrase; "(2x - y) as a factor" gives us the following information.
f(x, y) =(2x - y){some other factor(s)}
The phrase; "vanishing if x = -1 and y = 1" means that (x + y) must be one of the other factors. Start with:
(x + y)
substitute -1 for x and 1 for y:
-1 + 1 = 0
This factor will be zero, thereby, forcing the entire function to vanish (become zero).
Recapping what we know:
f(x, y) = (2x - y)(x + y){maybe some other factors}
Let's check the value of just the two factors when x = y = 1
f(1, 1) = (2{1} - {1})({1} + {1})
f(1, 1)= (2 - 1)(1 + 1)
f(1, 1) = (1)(2)
f(1, 1) = 2
This works so there are no other factors:
f(x, y) = (2x - y)(x + y)
Use the F.O.I.L. method to multiply the factors:
f(x, y) = 2x² + 2xy - xy - y²
Combine like terms:
f(x, y) = 2x² + xy - y²
Answered by
1
A is the correct option (2x^2+xy-y^2)
When x=-1 and y=1
Vanishing x= - 1 means
x+y is one of the factor.
-1+1
=0
Put f(x, y) than substitute in the equation (2x^2+xy-y^2)
We get,
0=>2(-1)^2+ (-1)(1)-(1)^2
0=>2(1)+(-1) -1
0=>2 - 1 - 1
0=>2-2
0=>0
Hence it is a factor and your ans is Option A.
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