\(a.101^2-99^2=\left(101+99\right)\left(101-99\right)=200.2=400\)

\(b.98.102=98.\left(100+2\right)=9800+196=9996\)

\(c,77^2+23^2+77.46=77^2+23^2+2.77.23=\left(77+23\right)^2=100^2=10000\)

101² = (100 + 1)² = 100² + 2.100.1 + 1² = 10000 + 200 + 1 = 10201

97 . 103 = (100 - 3)(100 + 3) = 100² - 3² = 10000 - 9 = 9991

77² + 2. 23. 77 + 23² = (77 + 23)² = 100² = 10000

105² - 5² = (105 - 5)(105 + 5) = 100 . 110 = 11000

tick nha

a) \(101^2\)

\(=\left(100+1\right)^2\)

\(=100^2+2.100.1+1^2\)

\(=10000+200+1\)

\(=10200+1\)

\(=10201\)

b) \(97.103\)

\(=\left(100-3\right).\left(100+3\right)\)

\(=100^2-3^2\)

\(=10000-9\)

\(=9991\)

c) \(77^2+23^2+77.46\)

\(=77^2+77.46+23^2\)

\(=77^2+2.77.23+23^2\)

\(=\left(77+23\right)^2\)

\(=100^2\)

\(=10000\)

d) \(105^2-5^2\)

\(=\left(105-5\right)\left(105+5\right)\)

\(=100.110\)

\(=11000\)

lâu lắm r moi lên h24, tớ giúp bn nhé:

*101² = (100+1)² = 10⁴ + 2.100.1 +1² = 10201

*97.103= (100-3)(100+3) = 10² - 3² = 9991

* = 77² + 2.77.23 + 23² = (77+23)² = 10⁴

1. a) 101² - 99² = (101 + 99)(101 - 99) = 200 . 2 = 400

b) 98.102 = (100 - 2)(100 + 2) = 100² - 4 = 10000 - 4 = 9996

c) 77² + 23² + 77.46 = 77² + 23² + 77.23.2 = (23 + 77)² = 100² = 10000

d) M = x³ + 9x² + 27x + 27 = (x + 3)³ = (7 + 3)³ = 10³ = 1000

2. a) 2x² + 3x - 5 = 0

=> 2x² + 5x - 2x - 5 = 0

=> x(2x + 5) - (2x + 5) = 0

=> (x - 1)(2x + 5) = 0

=> \(\orbr{\begin{cases}x-1=0\\2x+5=0\end{cases}}\)

=> \(\orbr{\begin{cases}x=1\\x=-\frac{5}{2}\end{cases}}\)

b) 2x² - 11x - 51 = 0

=> 2x² - 17x + 6x - 51 = 0

=> x(2x - 17) + 3(2x - 17) = 0

=> (x + 3)(2x - 17) = 0

=> \(\orbr{\begin{cases}x+3=0\\2x-17=0\end{cases}}\)

=> \(\orbr{\begin{cases}x=-3\\x=\frac{17}{2}\end{cases}}\)

a) 101² - 99² = (101-99)(101+99)= 2,200 = 4002

b)98.102 = (100-2)(100+2) = 100² - 2² =10000 - 4 = 9996

c) 77² + 23² +77.46 = 77² + 23² +2.77.23 = ( 77+23)² = 100² =1000

d) Với x=7 => M = 7³+ 9.7³ + 27.7 + 27 = 10.7³ +27.8 = 10.343 + 216 = 3430+216 = 3646

2. a) 2x² + 3x -5 =0

=> 2(x² +3/2 x +9/16) -49/8 = 0

=> 2 (x+3/4)² =49/8

=> (x+3/4)² =49/16 = (7/4)² = (-7/4)²

=> x+3/4 = 7/4 hoặc x+3/4 = -7/4

=> x= 1 hoặc x=-5/2

b) 2x² -11x - 51 =0

=> 2(x² -11/2x + 121/16) -529/8 = 0

=> (x -11/4)² = 529/16 = (23/4)² =(-23/4)²

=> x-11/4=23/4 hoặc x-11/4 = -23/4

=> x=17/2 hoặc x=-3

\(77^2+23+77.46\)

\(=77.77+23+77.46\)

\(=77.\left(77+46\right)+23\)

\(=77.123+23\)

\(=9471+23=9494\)

\(77^2+23+77.46\)

\(=77.77+23+77.46\)

\(=77.\left(77+46\right)+23\)

\(=77.123+23\)

\(=9471+23\)

\(=9494\)

77² + 23² + 77.46

= 23²+77.2.46+77²

=(23+77)²

=100²

=10000

77² + 23² + 77.46

= 77² + 2.77.23 + 23²

= (77 + 23)²

= 100²

= 10000

Tính nhanh

77² + 23² + 77.46=77²+2.77.23+23²=(77+23)²=100²=10000

\(a,=\dfrac{1}{3}\times\left(\dfrac{1}{2}+\dfrac{1}{3}\right)=\dfrac{1}{3}\times\dfrac{5}{6}=\dfrac{5}{18}\\ b,=\dfrac{4}{5}\times\left(\dfrac{1}{2}-\dfrac{1}{3}\right)=\dfrac{4}{5}\times\dfrac{1}{6}=\dfrac{2}{15}\\ c,=456\times99-6\times99+456\\ =456\times\left(99+1\right)-594\\ =456\times100-594=45600-594=45006\\ d,=101\times\left(101-1\right)=101\times100=10100\)