agar A+B+C =0 hua to 1/2A*A +BC+1/2B*B + CA+1/2C*C + AB=?​

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agar A+B+C =0 hua to 1/2A*A +BC+1/2B*B + CA+1/2C*C + AB=?​

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Kaylee 1 month 2021-08-13T03:11:22+00:00 2 Answers 0 views 0

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    0
    2021-08-13T03:13:06+00:00

    refer the attachment given above!!

    0
    2021-08-13T03:13:18+00:00

    Step-by-step explanation:

    a + b + c = 0

    ∴ a = -(b + c), b = -(c + a) , c = -(a + b)

    Now, (2a² + bc ) = (a² + a² + bc)

    = {a² + a(-b – c) + bc}

    = a² – ab – ac + bc = a(a – b) -c(a – c) = (a – c)(a – b) ————(1)

    similarly, (2b² + ca) = (b – c)(b – a) ————-(2)

    (2c² + ab) = (c – a)(c – b) ————–(3)

    now, LHS = 1/(2a² + bc ) + 1/(2b² + ca) + 1/(2c² + ab)

    = 1/(a – b)(a – c) + 1/(b – c)(b – a) + 1/(c – a)(c – b)

    = – 1/(a- b)(c – a) -1/(b – c)(a – b) – 1/(c – a)(b – c)

    = -[(b -c ) + (c – a) + (a – b)]/(a – b)(b – c)(c – a)]

    = 0 = RHS

    Hence, proved

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