show that (A.B)2+(A×B)2=A2B2
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Answer:
Assume that (a−b)
2
,(a
2
+b
2
) and (a+b)
2
are in AP.
So, difference between two consecutive terms will be same.
(a
2
+b
2
)−(a−b)
2
=(a+b)
2
−(a
2
+b
2
)
(a
2
+b
2
)−(a
2
+b
2
−2ab)=a
2
+b
2
+2ab−a
2
−b
2
2ab=2ab
Which is true.
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