Question

Prove that (a-b)^2,a^2+b^2,(a+b)^2 are in ap​

Answer 1

Answer:

if r will be 2ab then it can be proved

Answer 2

Answer:

Step-by-step explanation:

(a-b)²,a²+b²,(a+b)²

Here

(a-b)²=a²+b²-2ab

(a+b)²=a²+b²+2ab

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Let a²+b²=x and 2ab=y

then

(a-b)²=a²+b²-2ab=x-y

(a+b)²=a²+b²+2ab=x+y

Then the series becomes :

(a-b)², a²+b² and (a+b)²

are x-y, x and x+y

we observe

x-(x-y)=x-x+y=y

and x+y-x=y

Henece x-y, x and x+y are in AP

hence (a-b)², a²+b² and (a+b)² are in AP