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Question

If A=[1212],B=[2a1b] and if (A+B)2=A2+B2, find the values of a and b.

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Solution

A=[1212],B=[2a1b](A+B)=[1212]+[2a1b]=[32+a22+b](A+B)2=[32+a22+b][32+a22+b]=[52a2+a+2b+ab22bb22a4b]Now,A2=[1212][1212]=[1212]B2=[2a1b][2a1b]=[4a2a+ab2ba+b2]A2+B2=[1212]+[4a2a+ab2ba+b2]=[3a2+2a+ab1b2a+b]so,(A+B)2=A2+B2=[52a2+a+2b+ab22bb22a4b]=[3a2+2a+ab1b2a+b]52a=3aa=222b=1bb=1

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