2:5=6:?
Answers
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Answer:
funny pic
Step-by-step explanation:
x+y+xy=5...(i)
x
2
+y
2
+xy=7...(ii)
we know that a
2
+b
2
+2ab=(a+b)
2
Simplifying equation (ii)
x
2
+y
2
+xy=7
or, x
2
+y
2
+2xy−xy=7
or, (x+y)
2
−xy=7...(iii)
Simplifying equation (i)
x+y+xy=5
or, x+y=5−xy...(iv)
Putting this value of (x+y) in equation (iii)
(5−xy)
2
−xy=7
or, 25+x
2
y
2
−10xy−xy=7
or, x
2
y
2
−11xy+25−7=0
or x
2
y
2
−11xy+18=0
or, x
2
y
2
−2×xy×
2
11
+(
2
11
)
2
−(
2
11
)
2
+18=0
or, (xy−
2
11
)
2
−
4
121
+18=0
or, (xy−
2
11
)
2
−
4
49
or, (xy−
2
11
)=±
4
49
or, xy−
2
11
=±
2
7
When xy−
2
11
=+
2
7
xy=
2
7
+
2
11
xy=
2
18
xy=9...(v)
When xy−
2
11
=
2
−7
xy=
2
11
−
2
7
xy=
2
y
xy=2....(vi)
Hence, the solution of the given pair of equations
will be every pair of x & y which satisfies any of
the equations (v) or (vi)
So, there will be infinite solutions.