Bài giải:

a) x² + $\frac{1}{2}$x+ $\frac{1}{16}$ tại x = 49,75

Ta có: x² + $\frac{1}{2}$x+ $\frac{1}{16}$ = x² + 2 . x . $\frac{1}{4}$ + ${\left(\frac{1}{4}\right)}^2$= ${\left(x+\frac{1}{4}\right)}^2$

Với x = 49,75: ${\left(49,75+\frac{1}{4}\right)}^2$= (49,75 + 0,25)² = 50² = 2500

b) x² – y² – 2y – 1 tại x = 93 và y = 6

Ta có: x² – y² – 2y – 1 = x² – (y² + 2y + 1)

= x² - (y + 1)² = (x - y - 1)(x + y + 1)

Với x = 93, y = 6: (93 - 6 - 1)(93 + 6 + 1) = 86 . 100 = 8600

a) \(x^2+\dfrac{1}{2}x+\dfrac{1}{16}\) tại \(x = 49,75\)

Ta có : \(x^2+\dfrac{1}{2}x+\dfrac{1}{16}\) \(=\left(x^2+2.x.\dfrac{1}{4}+\left(\dfrac{1}{4}\right)^2\right)\)

\(=\left(x+\dfrac{1}{4}\right)^2\)

Khi \(x = 49,75\) ,ta có :

\(\left(49,75+\dfrac{1}{4}\right)^2\) \(=\left(\dfrac{200}{4}\right)^2\)

\(= 50^2\)

\(= 2500\)

b) \(x^2 - y^2 - 2y - 1\) tại \(x = 93\) và \(y = 6\)

Ta có : \(x^2 - y^2 - 2y - 1 = x^2 - (y^2 + 2y +1)\)

\(= x^2 - (y + 1)^2\)

\(= (x- y - 1) ( x+ y +1)\)

Khi \(x = 93\) và \(y = 6\) , ta có :

\((93 - 6 - 1) ( 93 + 6 + 1)\) \(= 86 . 100\)

\(= 8600\)

a)A=(x-y)x+y(x-y)=(x-y)(x+y)

Thay x=87,y=13 ta có:(87-13)(87+13)=74×100=7400

b)B=x^2+2x+1-y²=(x+1)²-y²=(x⁺1-y)(x+1+y)

Thay x=94,5,y=4,5 ta có (94,5+1-4,5)(94,5+1+4,5)=91.100=9100

c)C=x^2+1/2x+1/16=(x+1/4)²

^{thay x=49,75 ta có (49,75+1/4)^2=50^2=2500}

Bài 2:

a, \(5x\left(x-1\right)=x-1\)

\(\Leftrightarrow5x\left(x-1\right)-\left(x-1\right)=0\)

\(\Leftrightarrow\left(5x-1\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}5x-1=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{5}\\x=1\end{matrix}\right.\)

Vậy...

b, \(2\left(x+5\right)-x^2-5x=0\)

\(\Leftrightarrow2\left(x+5\right)-x\left(x+5\right)=0\)

\(\Leftrightarrow\left(2-x\right)\left(x+5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2-x=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-5\end{matrix}\right.\)

Vậy...

c, \(x^3-\dfrac{1}{4}x=0\)

\(\Leftrightarrow x\left(x^2-\dfrac{1}{4}\right)=0\)

\(\Leftrightarrow x\left(x-\dfrac{1}{2}\right)\left(x+\dfrac{1}{2}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-\dfrac{1}{2}=0\\x+\dfrac{1}{2}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{2}\\x=\dfrac{-1}{2}\end{matrix}\right.\)

Vậy...

Bài 3:

1, Đặt \(A=x^2+\dfrac{1}{2}x+\dfrac{1}{16}=x^2+\dfrac{1}{4}.x.2+\dfrac{1}{16}\)

\(=\left(x+0,25\right)^2\)

Thay x = 49,75 vào A ta có:
\(A=50^2=2500\)

2, tương tự

\(A=x^2-y^2-2y-1\)

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

\(=\left(93-6-1\right)\left(93+6+1\right)=86\cdot100=8600\)

B k hiểu đề là j

\(A=x^2-y^2-2y-1\)

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

\(=\left(93-6-1\right)\left(93+6+1\right)=86\times100=8600\)

B dạng tương tự

a) M = (x² + 3xy - 3x³) + (2y³ - xy + 3x³)

= x² + 3xy - 3x³ + 2y³ - xy + 3x³

= x² + (3xy - xy) + (-3x³ + 3x³) + 2y³

= x² + 2xy + 2y³

Tại x = 5 và y = 4

M = 5² + 2.5.4 + 2.4³

= 25 + 40 + 2.64

= 65 + 128

= 193

b) N = x²(x + y) - y(x² - y²)

= x³ + x²y - x²y + y³

= x³ + (x²y - x²y) + y³

= x³ + y³

Tại x = -6 và y = 8

N = (-6)³ + 8³

= -216 + 512

= 296

c) P = x² + 1/2 x + 1/16

= (x + 1/2)²

Tại x = 3/4 ta có:

P = (3/4 + 1/2)² = (5/4)² = 25/16

a: \(x^2+x-2x-2\)

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

\(=\left(x+1\right)\left(x-2\right)=\left(-1+1\right)\left(-1-2\right)=0\)

b: \(3x^2-2x+9x-6\)

\(=x\left(3x-2\right)+3\left(3x-2\right)\)

\(=\left(3x-2\right)\left(x+3\right)=\left(3\cdot7-2\right)\left(7+3\right)\)

\(=19\cdot10=190\)

c: \(2x^2-3xy-xy^2\)

\(=x\left(2x-3y-y^2\right)\)

\(=2\left(2\cdot2-3\cdot3-9\right)\)

\(=2\cdot\left(4-18\right)=-28\)