If x+y=10 and xy=12, find the value of x
2
−xy+y
2
.
- A74
- B82
- C64
- D78
Solution & Step-by-step Explanation
We know the algebraic identity:
(x+y)
2
=x
2
+2xy+y
2
Given x+y=10 and xy=12, substituting these values:
10
2
=x
2
+y
2
+2(12)
100=x
2
+y
2
+24
x
2
+y
2
=100−24=76
We need to find the value of x
2
−xy+y
2
:
x
2
−xy+y
2
=(x
2
+y
2
)−xy
x
2
−xy+y
2
=76−12=64
(x+y)
2
=x
2
+2xy+y
2
Given x+y=10 and xy=12, substituting these values:
10
2
=x
2
+y
2
+2(12)
100=x
2
+y
2
+24
x
2
+y
2
=100−24=76
We need to find the value of x
2
−xy+y
2
:
x
2
−xy+y
2
=(x
2
+y
2
)−xy
x
2
−xy+y
2
=76−12=64