the equations XY/X+Y=1/9 and XY/X-Y=1/4 are equivalent to the equations -1/X+1/Y=9;-1/X+1/Y=4,1/X-1/Y=9;-1/X-1/Y=4,1/X+1/Y=-4;1/X+1/Y=-9,1/X+1/Y=9;-1/X+1/Y=4
Answers
Step-by-step explanation:
Correct option is
C
x+y+z
∣
∣
∣
∣
∣
∣
∣
∣
x
y
z
x
3
y
3
z
3
x
4
−1
y
4
−1
z
4
−1
∣
∣
∣
∣
∣
∣
∣
∣
=0
xyz
∣
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∣
∣
∣
∣
∣
∣
1
1
1
x
2
y
2
z
2
x
3
y
3
z
3
∣
∣
∣
∣
∣
∣
∣
∣
−1
∣
∣
∣
∣
∣
∣
∣
∣
x
y
z
x
3
y
3
z
3
1
1
1
∣
∣
∣
∣
∣
∣
∣
∣
=0
R
1
→R
1
−R
3
,R
2
→R
2
−R
3
(x−y)(y−z)xyz
∣
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∣
∣
∣
0
0
1
x+z
y+z
z
2
x
2
+xz+z
2
y
2
+yz+z
2
z
3
∣
∣
∣
∣
∣
∣
∣
∣
−(x−y)(y−z)
∣
∣
∣
∣
∣
∣
∣
∣
1
1
z
x
2
+xz+z
2
y
2
+yz+z
2
z
3
0
0
1
∣
∣
∣
∣
∣
∣
∣
∣
=0
⇒xyz
∣
∣
∣
∣
∣
∣
∣
∣
0
0
1
x+z
y+z
z
2
x
2
+xz+z
2
y
2
+yz+z
2
z
3
∣
∣
∣
∣
∣
∣
∣
∣
−
∣
∣
∣
∣
∣
∣
∣
∣
1
1
z
x
2
+xz+z
2
y
2
+yz+z
2
z
3
0
0
1
∣
∣
∣
∣
∣
∣
∣
∣
=0 ( ∵x
=y
=z)
R
1
→R
1
−R
2
xyz(x−y)
∣
∣
∣
∣
∣
∣
∣
∣
0
0
1
1
y+z
z
2
(x+y+z)
y
2
+yz+z
2
z
3
∣
∣
∣
∣
∣
∣
∣
∣
−(x−y)
∣
∣
∣
∣
∣
∣
∣
∣
0
1
z
(x+y+z)
y
2
+yz+z
2
z
3
0
0
1
∣
∣
∣
∣
∣
∣
∣
∣
=0
⇒−xyz(x−y)(xy+yz+xz)+(x−y)(x+y+z)=0
⇒xyx(xy+yz+xz)=x+y+z (∵x
=y)