Question

Hỏi nhiều mà chẳng ai trả lời chán

phân tích : x⁸+98x⁴+1

Answer 1

x⁸+98x⁴+1

= (x⁸+2x⁴+1)+96x⁴

= (x⁴+1)²+96x⁴

= (x⁴+1)²+16x²(x⁴+1) - 16x²(x⁴+1) +64x⁴+32x⁴

= [(x⁴+1)²+16x²(x⁴+1) +64x⁴]-16x²(x⁴+1)+32x⁴

= (x⁴+8x²+1)²-16x²(x⁴+1-2x²)

= (x⁴+8x²+1)²-16x²(x²-1)²

= (x⁴+8x²+1)² - (4x³-4x)²

= (x⁴+4x³+8x²-4x+1)(x⁴-4x³+8x²+4x+1)

Answer 2

\(x^8+98x^4+1\)

\(=x^8+98x^4+2401-2400\)

\(=\left[\left(x^4\right)^2+2.x^4.49+49^2\right]-2400\)

\(=\left(x^4+49\right)^2-\left(\sqrt{2400}\right)^2\)

\(=\left(x^4+49-\sqrt{2400}\right)\left(x^4+49+\sqrt{2400}\right)\)