Question

(2x + 3y - 5)² + (3x + 2y - 5)²=0...prove it​

Answer 1

Answer:

Correct option is

D

3x

2

+4xy+3y

2

−10x−10y=c

put y=y+k;x=x+h

⇒3h+2k−5=0 ... (1)

2h+3k−5=0 .. (2)

⇒

dx

dy

+

2x+3y

3x+2y

=0

put y=vx

⇒v+x

dx

dv

+

2+3v

3+2v

=0

⇒x

dx

dv

+

2+3v

3+4v+3v

2

=0

⇒∫2

3v

2

+4v+3

(2+3v)

dv+∫2

x

dx

=c

⇒logx

2

(3v

2

+4v+3)=c

⇒x

2

(3v

2

+4v+3)=c

⇒3y

2

+4yx+3x

2

=c

⇒3(y−k)

2

+4(y−k)(x−h)+3(x−h)

2

=c

⇒3x

2

+3y

2

+4xy+x(−6h−4k)+y(−6k−4h)=c

⇒3x

2

+3y

2

+4xy−10x−10y=c . From (1) and (2)

Answer 2

HOPE THIS WILL HELP YOU.