If x+y=18 and xy=9, then the value of (
y
x
+
x
y
) will be:
- A32
- B38
- C34
- D36
Solution & Step-by-step Explanation
We need to find the value of:
y
x
+
x
y
=
xy
x
2
+y
2
We know from algebraic identities that:
x
2
+y
2
=(x+y)
2
−2xy
Given x+y=18 and xy=9, substitute these values:
x
2
+y
2
=(18)
2
−2(9)
x
2
+y
2
=324−18=306
Now, substitute back into our original objective fraction:
xy
x
2
+y
2
=
9
306
=34
y
x
+
x
y
=
xy
x
2
+y
2
We know from algebraic identities that:
x
2
+y
2
=(x+y)
2
−2xy
Given x+y=18 and xy=9, substitute these values:
x
2
+y
2
=(18)
2
−2(9)
x
2
+y
2
=324−18=306
Now, substitute back into our original objective fraction:
xy
x
2
+y
2
=
9
306
=34