Toán 3 ( x mũ 4 + x mũ 2 + 1 ) – ( x mũ 2 +x+1) mũ 2 09/07/2021 By Arianna 3 ( x mũ 4 + x mũ 2 + 1 ) – ( x mũ 2 +x+1) mũ 2
$3.(x^4+x^2+1)-(x^2+x+1)^2_{}$ $⇔3x^4+3x^2+3-(x^4+x^2+1+2x^3+2x^2+2x)_{}$ $⇔3x^4+3x^2+3-x^4-x^2-1-2x^3-2x^2-2x_{}$ $⇔2x^4-2x^3-2x+2_{}$ $⇔2x^3.(x-1)-2.(x-1)_{}$ $⇔(x-10).(2x^3-2)_{}$ $⇔2.(x-1)(x^3-1)_{}$ Trả lời
Áp dụng HĐT mở rộng: (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac ——————– 3(x^4 + x^2 + 1) – (x^2 + x + 1)^2 = (3x^4 + 3x^2 + 3) – (x^4 + x^2 + 1 + 2x^3 + 2x^2 + 2x) = 3x^4 + 3x^2 + 1 – x^4 – x^2 – 1 – 2x^3 – 2x^2 – 2x = (3x^4 – x^4) + 2x^3 + (3x^2 – x^2 – 2x^2) – 2x + (1 – 1) = 2x^4 + 2x^3 – 2x @vietdorapan Trả lời
$3.(x^4+x^2+1)-(x^2+x+1)^2_{}$
$⇔3x^4+3x^2+3-(x^4+x^2+1+2x^3+2x^2+2x)_{}$
$⇔3x^4+3x^2+3-x^4-x^2-1-2x^3-2x^2-2x_{}$
$⇔2x^4-2x^3-2x+2_{}$
$⇔2x^3.(x-1)-2.(x-1)_{}$
$⇔(x-10).(2x^3-2)_{}$
$⇔2.(x-1)(x^3-1)_{}$
Áp dụng HĐT mở rộng: (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac
——————–
3(x^4 + x^2 + 1) – (x^2 + x + 1)^2
= (3x^4 + 3x^2 + 3) – (x^4 + x^2 + 1 + 2x^3 + 2x^2 + 2x)
= 3x^4 + 3x^2 + 1 – x^4 – x^2 – 1 – 2x^3 – 2x^2 – 2x
= (3x^4 – x^4) + 2x^3 + (3x^2 – x^2 – 2x^2) – 2x + (1 – 1)
= 2x^4 + 2x^3 – 2x
@vietdorapan