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Toán Lớp 8: Cho a+b+c=0 CMR: ($a^{2}$ +$b^{2}$+ $c^{2}$)^2=2($a^{4}$ +$b^{4}$+ $c^{4}$)

Home/ Toán Lớp 8: Cho a+b+c=0 CMR: ($a^{2}$ +$b^{2}$+ $c^{2}$)^2=2($a^{4}$ +$b^{4}$+ $c^{4}$)

Toán Lớp 8: Cho a+b+c=0 CMR: ($a^{2}$ +$b^{2}$+ $c^{2}$)^2=2($a^{4}$ +$b^{4}$+ $c^{4}$)

Hồng Tháng Một 29, 2023 Toán học 1 Comment 0 views

Toán Lớp 8: Cho a+b+c=0 CMR:
($a^{2}$ +$b^{2}$+ $c^{2}$)^2=2($a^{4}$ +$b^{4}$+ $c^{4}$)

Comments ( 1 )

maianhnhiquynh
29 Tháng Một, 2023 at 11:51 chiều

Reply

Giải đáp:

a+b+c=0

<=>(a+b+c)^2=0

<=>a^2+b^2+c^2+2ab+2bc+2ca=0

<=>a^2+b^2+c^2=-(2ab+2bc+2ca)

<=>(a^2+b^2+c^2)^2=(2ab+2bc+2ca)^2

<=>a^4+b^4+c^4+2a^2b^2+2b^2c^2+2c^2a^2=4a^2b^2+4b^2c^2+4c^2a^2+8ab^2c+8abc^2+8a^2bc

<=>a^4+b^4+c^4=2a^2b^2+2b^2c^2+2c^2a^2+8abc(a+b+c)

<=>a^4+b^4+c^4=2a^2b^2+2b^2c^2+2c^2a^2

<=>a^4+b^4+c^4+2a^2b^2+2b^2c^2+2c^2a^2=2a^4+2b^4+2c^4

<=>(a^2+b^2+c^2)^2=2(a^4+b^4+c^4)

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