If a+b=10 and a
2
+b
2
=58, then find ab.
- A21
- B24
- C25
- D16
Solution & Step-by-step Explanation
We use the algebraic identity:
(a+b)
2
=a
2
+b
2
+2ab
Given:
a+b=10
a
2
+b
2
=58
Substitute these values into the identity:
(10)
2
=58+2ab
100=58+2ab
2ab=100−58
2ab=42
ab=21
(a+b)
2
=a
2
+b
2
+2ab
Given:
a+b=10
a
2
+b
2
=58
Substitute these values into the identity:
(10)
2
=58+2ab
100=58+2ab
2ab=100−58
2ab=42
ab=21