If x−y=6 and xy=40, then find x
2
+y
2
.
- A116
- B80
- C89
- D146
Solution & Step-by-step Explanation
We use the standard algebraic identity:
(x−y)
2
=x
2
+y
2
−2xy
Substitute the given values x−y=6 and xy=40 into the equation:
(6)
2
=x
2
+y
2
−2(40)
36=x
2
+y
2
−80
x
2
+y
2
=36+80
x
2
+y
2
=116
(x−y)
2
=x
2
+y
2
−2xy
Substitute the given values x−y=6 and xy=40 into the equation:
(6)
2
=x
2
+y
2
−2(40)
36=x
2
+y
2
−80
x
2
+y
2
=36+80
x
2
+y
2
=116