a) A = 18x + 17y = 19x + 19y - (x + 2y) = 19(x + y) - (x + 2y) = 19(x + y) - B

Vậy A chia hết cho 19 khi và chỉ khi B chia hết cho 19.

b) Tương tự, M = 3a - b = 5a - 5b - 2a + 4b = 5(a - b) - 2(a - 2b)

2 không chia hết cho 5 nên M chia hết cho 5 khi và chỉ khi  a - 2b chia hết cho 5.

c) Tương tự: P = 3x² - 10y = 13x²  - 10x² - 10y = 13x² - 10(x² + y)

10 không chia hết cho 13 nên P chia hết cho 13 khi và chỉ khi x² + y chia hết cho 13.

b,Hướng dẫn: Xét A+b or A-B or mA+nB or mA-nB

\(B=\left(x^2+4xy+4y^2\right)-\left(2x+4y\right)+10\)

    \(=\left(x+2y\right)^2-2\left(x+2y\right)+10\)

    \(=5^2-2.5+10\)

      \(=25\)

  B = (3 + 1).(3² + 1).(3⁴ + 1).(3⁸ + 1).(3¹⁶ + 1)

2B = (3 - 1).(3 + 1).(3² + 1).(3⁴ + 1).(3⁸ + 1).(3¹⁶ + 1)

     = (3² - 1).(3² + 1).(3⁴ + 1).(3⁸ + 1).(3¹⁶ + 1)

     = (3⁴ - 1).(3⁴ + 1).(3⁸ + 1).(3¹⁶ + 1)

     = (3⁸ - 1).(3⁸ + 1).(3¹⁶ + 1)

     = (3¹⁶ - 1).(3¹⁶ + 1)

     = 3³² - 1

Vậy A = B

lộn r` bn B = 3³²-1 / 2

Vậy A > B

\(P=\frac{1}{2}\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

    \(=\frac{1}{2}\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

     \(=\frac{1}{2}\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

     \(=\frac{1}{2}\left(5^{16}-1\right)\left(5^{16}+1\right)\)

       \(=\frac{1}{2}\left(5^{32}-1\right)\)

Ta có:   \(P=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

     \(\Leftrightarrow P=\frac{\left(5^2-1\right)}{2}\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

     \(\Leftrightarrow P=\frac{1}{2}\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

      \(\Leftrightarrow P=\frac{1}{2}\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

      \(\Leftrightarrow P=\frac{1}{2}\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

       \(\Leftrightarrow P=\frac{1}{2}\left(5^{16}-1\right)\left(5^{16}+1\right)\)

       \(\Leftrightarrow P=\frac{5^{32}-1}{2}\)

Vậy \(P=\frac{5^{32}-1}{2}\)

2x² + 3 ( x - 1 ) ( x - 1 ) = 5x( x + 1 )

=>2x²+3x²-6x+3=5x²+5x

=>5x²-6x+3=5x²+5x

=>(5x²-5x²)-6x-5x=0-3

=>-11x=-3

=>x=3/11