যদি a 2 - bc = α, b 2 - ac = β, c 2 - ab = γ, তাহলে -এর সমান কত?

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Question

This question was previously asked in

CDS Elementary Mathematics 3 Sep 2023 Official Paper

Answer 1

সূত্র ব্যবহৃত:

a 3 + b 3 + c 3 - 3abc = (a + b +c)(a 2 + b 2 + c 2 - ab - bc - ac)

গণনা:

a 2 - bc = α ] × a

a 3 - abc = aα ------(1)

b 2 - ac = β ] × b

b 3 - abc = bβ ------(2)

c 2 - ab = γ ] × c

c 3 - abc = cγ ------(3)

সমীকরণ (1), (2) এবং (3) যোগ করে

a 3 + b 3 + c 3 - 3abc = aα + bβ + cγ

a 2 - bc + b 2 - ac + c 2 - ab = α + β + γ

⇒ =

∴ = 1