If x−y=−9 and xy=−20, then find x
2
+y
2
.
- A61
- B41
- C85
- D113
Solution & Step-by-step Explanation
We can use the standard algebraic identity:
(x−y)
2
=x
2
+y
2
−2xy
We are given x−y=−9 and xy=−20. Let's substitute these values into the identity:
(−9)
2
=x
2
+y
2
−2(−20)
81=x
2
+y
2
+40
Rearranging to solve for x
2
+y
2
:
x
2
+y
2
=81−40
x
2
+y
2
=41
(x−y)
2
=x
2
+y
2
−2xy
We are given x−y=−9 and xy=−20. Let's substitute these values into the identity:
(−9)
2
=x
2
+y
2
−2(−20)
81=x
2
+y
2
+40
Rearranging to solve for x
2
+y
2
:
x
2
+y
2
=81−40
x
2
+y
2
=41