Question

Show that $(a-b)^{2}, (a^{2}+b^{2}) and(a+b)^{2}$ are in A.P.

Answer 1

Answer:  Step-by-step explanation:

Given numbers are :  

( a - b )² , ( a² + b² ) & ( a + b )²

We have to show that these given numbers are in AP.

If the numbers are in AP then their common difference must be same.

Second term - first term =  third term - second term

a2 - a1 = a3 - a2

=>(a² + b² ) - (a - b )² = (a + b )² - (a² + b²)

=>a² + b² - (a² - 2ab + b² ) = a² + b² + 2ab - a² - b²

=>a² + b² - a² + 2ab - b² = a² - a² + b² - b² +  2ab

=> 2ab  = 2ab  

Here ,common difference is same

Hence, the given numbers are in A.P.

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Answer 2

Answer:

hence proved

Step-by-step explanation:

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