x⁸ + 98x⁴ + 1

= (x⁸ + 2x⁴ + 1 ) + 96x⁴
= (x⁴ + 1)² + 16x²(x4 + 1) + 64x⁴ - 16x²(x⁴ + 1) + 32x⁴
= (x⁴ + 1 + 8x²)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)

Vì \(x=99\Rightarrow98=x-1\)

Thay \(98=x+1\)vào biểu thức A , ta có :

\(A=x^7-\left(x-1\right)x^6-\left(x-1\right)x^5-\left(x-1\right)x^4-\left(x-1\right)x^3-\left(x-1\right)x^2-\left(x-1\right)x+1\)

\(\Rightarrow A=x^7-x^7+x^6-x^6+x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x+1\)

\(\Rightarrow A=x+1=99+1=100\)

a) \(x^8+14x^4+1=\left(x^4+1\right)^2+12x^4=\left(x^4+1\right)^2+4x^2\left(x^4+1\right)+4x^4-4x^2\left(x^4+1\right)+8x^4\)

\(=\left(x^4+2x^2+1\right)^2-4x^2\left(x^4-2x^2+1\right)=\left(x^4+2x^2+1\right)^2-\left(2x\left(x^2-1\right)\right)^2\)

\(=\left(x^4-2x^3+2x^2+2x+1\right)\left(x^4+2x^3+2x^2-2x+1\right)\)

Tại x = 99

\(a,x^8+14x^4+1=\left(x^8+14x^4+49\right)-48\)

\(=\left(x^4+7\right)^2-48\)

\(=\left(x^4+7+\sqrt{48}\right)\left(x^4+7-\sqrt{48}\right)\)

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

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

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

\(=\left(x^4+49+20\sqrt{6}\right)\left(x^4+49-20\sqrt{6}\right)\)

Mình nghĩ vậy k bt đúng k :)

Ta có : \(x^8+14x^4+1\)

\(=x^8+2.x^4.7+1\)

\(=x^8+2.x^4.7+49-48\)

\(=\left(x^4+7\right)^2-48\)

\(=\left(x^4+7-\sqrt{48}\right)\left(x^4+7+\sqrt{48}\right)\)

a/\(=\left(x^4+1\right)^2+12x^4=\left(x^4+1\right)^2+4x^2\left(x^4+1\right)+4x^4-4x^2\left(x^4+1\right)+8x^4\)

\(=\left(x^4+1+2x^2\right)^2-4x^2\left(x^4+1-2x^2\right)=\left(x^4+2x^2+1\right)-\left(2x^3-2x\right)^2\)

\(=\left(x^4+2x^3+2x^2-2x+1\right)\left(x^4-2x^3+2x^2+2x+1\right)\)

b/\(=\left(x^4+1\right)^2+96x^4=\left(x^4+1\right)^2+16x^2\left(x^4+1\right)+64x^4-16x^2\left(x^4+1\right)+32x^4\)

\(=\left(x^4+1+8x^2\right)^2-16x^2\left(x^4+1-2x^2\right)=\left(x^4+8x^2+1\right)-\left(4x^3-4x\right)^2\)

\(=\left(x^4+4x^3+8x^2-4x+1\right)\left(x^4-4x^3+8x^2+4x+1\right)\)

x⁸ + 98x⁴ + 1

= (x⁸ + 2x⁴ + 1 ) + 96x⁴
= (x⁴ + 1)² + 16x²(x⁴ + 1) + 64x⁴ - 16x²(x⁴ + 1) + 32x⁴
= (x⁴ + 1 + 8x²)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)

x⁸ + 98x⁴ + 1

= (x⁸ + 2x⁴ + 1 ) + 96x²

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

= (x⁴ + 1 + 8x²)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)

Vậy...

Nhầm! Dòng 2 phải là 96.x⁴

https://coccoc.com/search/math#query=Ph%C3%A2n+t%C3%ADch+%C4%91a+th%E1%BB%A9c+th%C3%A0nh+nh%C3%A2n+t%E1%BB%AD%3A+x%5E8%2B98x%5E4%2B1

x8 + 98x4 + 1 = (x8 + 2x4 + 1 ) + 96x4

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

= (x4 + 1 + 8x2)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)