\(a^{10}+a^5+1\)

\(=\left(a^{10}-a\right)+\left(a^5-a^2\right)+\left(a^2+a+1\right)\)

\(=a\left(a^3-1\right).\left(a^6+a^3+1\right)+a^2\left(a^3-1\right)+\left(a^2+a+1\right)\)

\(=a\left(a-1\right)\left(a^2+a+1\right)+\left(a^6+a^3+1\right)+a^2\left(a-1\right)\left(a^2+a+1\right)\)+  (a²+a+1) 

Đến đây rùi thì tự làm tiếp nha

\(a^{10}+a^5+1\)

\(=\left(a^{10}+a^9+a^8\right)-\left(a^9+a^8+a^7\right)+\left(a^7+a^6+a^5\right)-\left(a^6+a^5+a^4\right)+\left(a^5+a^4+a^3\right)-\left(a^3+a^2+a\right)+\left(a^2+a+1\right)\)\(=\left(a^2+a+1\right)\left(a^8-a^7+a^5-a^4+a^3-a+1\right)\)

x^4+x^2+1 = (x^4+2x^2+1)-x^2 = (x^2+1)^2-x^2 = (x^2-x+1).(x^2+x+1)

k mk nha

bạn ơi bạn chưa bớt 2x^2 kìa

ngu dốt

x⁵-x⁴-1=x⁵-x³-x²-x⁴+x²+x+x³-x-1

=x².(x³-x-1)-x.(x³-x-1)+(x³-x-1)

=(x³-x-1)(x²-x+1)

x^4+x^2+1 = (x^4+2x^2+1)-x^2 = (x^2+1)^2-x^2 = (x^2-x+1).(x^2+x+1)

k mk nha

mik chịu

x^10+x^5+1

=x¹⁰-x+x⁵-x²+x²+x+1

=x.(x⁹-1)+x².(x³-1)+(x²+x+1)

=x.(x³-1)(x³+1)+x²(x³-1)+(x²-x+1)

=x.(x-1)(x²+x+1)(x³+1)+x²(x-1)(x²+x+1)+(x²+x+1)

=(x²+x+1)[x.(x-1)(x³+1)+x²(x-1)+1]

=(x²+x+1)(x⁵+x²-x⁴-x+x³-x²+1)

=(x²+x+1)(x⁵-x⁴+x³-x+1)

x^10+x^5+1

=x¹⁰-x+x⁵-x²+x²-x+1

=x.(x⁹-1)+x².(x³-1)+(x²+x+1)

=x.(x³-1)(x³+1)+x²(x³-1)+(x²-x+1)

=x.(x-1)(x²+x+1)(x³+1)+x²(x-1)(x²+x+1)+(x²+x+1)

=(x²+x+1)[x.(x-1)(x³+1)+x²(x-1)+1]

=(x²+x+1)(x⁵+x²-x⁴-x+x³-x²+1)

=(x²+x+1)(x⁵-x⁴+x³-x+1)

sai rồi

\(a^{10}+a^5+1\)

\(a^{10}+a^5+1=\left(a^2+a+1\right)\left(a^8-a^7+a^5-a^4+a^3-a+1\right)\)

\(x^{10}+x^5+1\)

\(=x^{10}+x^9+x^8-x^9-x^8-x^7+x^7+x^6+x^5-x^6-x^5-x^4+x^5+x^4+x^3-x^3-x^2-x+x^2+x+1\)

\(=x^8\left(x^2+x+1\right)-x^7\left(x^2+x+1\right)+x^5\left(x^2+x+1\right)-x^4\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x\left(x^2+x+1\right)+\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^8-x^7+x^5-x^4+x^3-x+1\right)\)

x¹⁰ + x⁵ + 1 = (x¹⁰ - x) + (x⁵ - x²) + (x² + x + 1) = x.[(x³)³ - 1] + x².(x³ - 1) + (x² + x + 1)

= x.(x³ - 1).(x⁶ + x³ + 1) + x².(x³ - 1) + (x² + x + 1)

= (x² + x + 1). [x.(x -1).(x⁶ + x³ + 1) + x² + 1 ]

mình làm tương tự mấy ban kia nha

k tui nha

thannks

 a¹⁰ + a⁵ + 1

= a¹⁰ - a⁹ + a⁷ - a⁶ + a⁵ - a³ + a² + a⁹ - a⁸ + a⁶ - a⁵ + a⁴ - a³ + a + a⁸ - a⁷ + a⁵ - a⁴ + a² - a + 1 

nhóm 7 hạng tử ta đc : 

= a²(a⁸ - a⁷ + a⁵ - a⁴ + a³ - a + 1) + a(a⁸ - a⁷ + a⁵ - a⁴ + a³ - a + 1) + (a⁸ - a⁷ + a⁵ - a⁴ + a³ - a + 1)

= (a² + a + 1)(a⁸ - a⁷ + a⁵ - a⁴ + a³ - a + 1)

                   = x.(x³ - 1).(x⁶ + x³ + 1) + x².(x³ - 1) + (x² + x + 1)

                   = (x² + x + 1). [x.(x -1).(x⁶ + x³ + 1) + x² + 1 ]

hơi dài tí ^^

 a¹⁰ + a⁵ + 1

= a¹⁰ - a⁹ + a⁷ - a⁶ + a⁵ - a³ + a² + a⁹ - a⁸ + a⁶ - a⁵ + a⁴ - a³ + a + a⁸ - a⁷ + a⁵ - a⁴ + a² - a + 1 

nhóm 7 hạng tử ta đc : 

= a²(a⁸ - a⁷ + a⁵ - a⁴ + a³ - a + 1) + a(a⁸ - a⁷ + a⁵ - a⁴ + a³ - a + 1) + (a⁸ - a⁷ + a⁵ - a⁴ + a³ - a + 1)

= (a² + a + 1)(a⁸ - a⁷ + a⁵ - a⁴ + a³ - a + 1)

ĐKXĐ : \(-4\le x\le4\)

\(\Rightarrow\frac{x^3}{\sqrt{16-x^2}}=16-x^2\)

\(\Rightarrow x^3=\left(16-x^2\right)\left(\sqrt{16-x^2}\right)\)

\(\Rightarrow x^3=\left(\sqrt{16-x^2}\right)^3\)

\(\Rightarrow x=\sqrt{16-x^2}\)

\(\Rightarrow16-x^2=x^2\)

\(\Rightarrow2x^2=16\Rightarrow x^2=8\Rightarrow x=+-\sqrt{8}\)(thỏa)