Question

please answer this question
I will mark you brainliest

Answer 1

2 answers · Mathematics 

 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

Answer 2

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.