find the greatest comman factor in the following
a) x³y² + x²y³ - xy⁴ + xy
b) 2xy, -y², 2x²y
PLEASE PROVIDE A VALID AND A CORRECT ANSWER.
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Answer:
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Step-by-step explanation:
we have
x+y
2xy
=
2
3
....(i)
2x−y
xy
=
10
−3
....(ii)
[(x+y)
=0 and (2x−y)
=0)]
Inversing the eqn (i) we get
2xy
x+y
=
3
2
⇒
2xy
x
+
2xy
y
=
3
2
⇒
2y
1
+
2x
1
=
3
2
....(iii)
Inversing the eqn (ii) we get
xy
2x−y
=
−3
10
⇒
xy
2x
−
xy
y
=
3
−10
⇒
y
2
−
x
1
=
3
−10
⇒
2y
2
−
2x
1
=
3
−5
...(iv)
now,
2y
2
−
2x
1
=
3
−5
[ from (iv) ]
2y
1
−
2x
1
=
3
2
[ from (ii) ]
and ______________________
2y
2
+
2y
1
=−
3
5
+
3
2
[ adding (iii) and (iv)]
⇒
2y
2+1
=
3
−5+2
⇒
2y
3
=
3
−3
⇒
2y
3
=−1⇒y=−
3
3
now
2y
2
−
2x
1
=
3
−5
⇒
y
2
−
x
1
=
3
−10
⇒
(
2
−3
)
2
−
x
1
=
3
−10
[∵y=
2
−3
]
⇒
−3
4
−
x
1
=
3
−10
⇒−
x
1
=
3
−10
+
3
4
⇒
x
−1
=
3
−6
⇒
x
1
=
1
+2
⇒2x=1⇒x=
2
1
So , x=
2
1
and y=
2
−3
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