2016 - x : 3 = 435

             x : 3 = 2016 - 435

             x : 3 = 1581

              x = 1581 x 3 = 4743

Ta có: f(0) = 1 => f(0) = d = 1

f(-1) = 2 => f(-1) = -a + b - c + d = 2 => -a + b - c = 1

=> a = b - c - 1 (1)

f(1/2) = 3 => f(1/2) = 1/8a+ 1/4b + 1/2c + d = 3

=> 1/8a + 1/4b + 1/2c = 2 =>a + 2b + 4c = 16 (2)

f(1) = 7 => f(1) = a + b + c + d = 7 => a + b + c = 6 (3)

Thay (1) vào (2) và (3)

(2) b - c + 1 + 2b + 4c = 16 => 3b + 3c = 15 => b + c = 5

(3) b - c + 1 + b + c = 6 -> 2b = 5 => b = 5/2

=> c = 5 - 5/2 = 5/2

=> a = b - c + 1 = 5/2 - 5/2 + 1 = 1

\(B=\dfrac{2}{1\times3}+\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+\dfrac{2}{7\times9}+...+\dfrac{2}{99\times101}\)

\(B=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+....+\dfrac{1}{99}-\dfrac{1}{101}\)

\(B=1-\dfrac{1}{101}=\dfrac{100}{101}\)

Đk: \(x\ge2+\sqrt{3}\)

Ta có: \(x+1+\sqrt{x^2-4x+1}=3\sqrt{x}\)

<=> \(x-4+\sqrt{x^2-4x+1}-1-3\left(\sqrt{x}-2\right)=0\)

<=> \(x-4+\dfrac{x\left(x-4\right)}{\sqrt{x^2-4x+1}+1}-\dfrac{3\left(x-4\right)}{\sqrt{x}+2}=0\)

<=> \(\left(x-4\right).\left(1+\dfrac{x}{\sqrt{x^2-4x+1}+1}-\dfrac{3}{\sqrt{x}+2}\right)=0\)

<=> \(x=4\)

Vì \(x\ge2+\sqrt{3}\) -> \(\dfrac{x}{\sqrt{x^2-4x+1}}>0\); \(-\dfrac{3}{\sqrt{x}+2}>-1\)

=> \(1+\dfrac{x}{\sqrt{x^2-4x+1}}-\dfrac{3}{\sqrt{x}+2}>0\)

Ta có:

a + b + c = 0

<=> a² + b² + c² + 2(ab + bc + ac) = 0

<=> ab + bc + ac = -7

<=> a²b² + b²c² + a²c²  + 2abc(a + b + c) = 49

<=> a²b² + b²c² + a²c² = 49 (vì a + b + c = 0)

<=> 2(a²b² + b²c² + a²c²) = 98

<=> (a² + b² + c²)² = 98 + a⁴ + b⁴ + c⁴

<=> a⁴ + b⁴ + c⁴ = 14² - 98 = 98

Mảnh vải còn lại là: 

   98 - 35 = 63 (cm)

Mảnh vải còn lại dài hơn số đã cắt là: 

    63 - 35 = 28 (cm)

      Đ/s: 28 cm

Với x < 0 và y > = 0, Ta có:

M = 3x + 3|x| - 5y + 5|y| + 6 = 3x - 3x - 5y + 5y + 6 = 6

Ta có: \(\dfrac{2}{x^2+y^2}=\dfrac{x^2+y^2+z^2}{x^2+y^2}=1+\dfrac{z^2}{x^2+y^2}\le1+\dfrac{z^2}{2xy}\)(bđt cosi)

CMTT: \(\dfrac{2}{y^2+z^2}\le1+\dfrac{x^2}{2yz}\); \(\dfrac{2}{z^2+x^2}\le1+\dfrac{y^2}{2xz}\)

=> \(\dfrac{2}{x^2+y^2}+\dfrac{2}{y^2+z^2}+\dfrac{2}{z^2+x^2}\le3+\dfrac{z^2}{2xy}+\dfrac{x^2}{2yz}+\dfrac{y^2}{2xz}=3+\dfrac{x^3+y^3+z^3}{2xyz}\) (Đpcm)