a) \(x^4-x^2+\dfrac{1}{4}-\dfrac{225}{4}=0\\ \left(x^2-\dfrac{1}{2}\right)^2-\dfrac{15}{2}^2=0\\ \left(x+7\right)\left(x-8\right)=0\\ \left[{}\begin{matrix}x=8\\x=-7\end{matrix}\right.\)

Vậy x = 8 hoặc x = -7

a: Ta có: \(x^4-x^2-56=0\)

\(\Leftrightarrow x^4-8x^2+7x^2-56=0\)

\(\Leftrightarrow\left(x^2-8\right)\left(x^2+7\right)=0\)

\(\Leftrightarrow x^2-8=0\)

hay \(x\in\left\{2\sqrt{2};-2\sqrt{2}\right\}\)

\(2017\cdot \left(225-1^2\right)\left(225-2^2\right)....\left(225-15^2\right).....\left(225-56^2\right)\)

\(=2017\cdot224\cdot221\cdot\cdot\cdot\cdot\cdot0\cdot\cdot\cdot\left(-2911\right)\)

\(=0\)

\(\frac{1}{11\times16}+\frac{1}{16\times21}+\frac{1}{21\times26}+...+\frac{1}{56\times61}+\frac{1}{61\times66}\)

\(=\frac{1}{5}\times\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{56}-\frac{1}{61}+\frac{1}{61}-\frac{1}{66}\right)\)

\(=\frac{1}{5}\times\left(\frac{1}{11}-\frac{1}{66}\right)\)

\(=\frac{1}{5}\times\frac{5}{66}\)

\(=\frac{1}{66}\)

\(\frac{1}{11\times16}+\frac{1}{16\times21}+\frac{1}{21\times26}+...+\frac{1}{56\times61}+\frac{1}{61\times66}\)

\(=\frac{1}{5}\times\left(\frac{5}{11\times16}+\frac{5}{16\times21}+\frac{5}{21\times26}+...+\frac{5}{56\times61}+\frac{5}{61\times66}\right)\)

\(=\frac{1}{5}\times\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{56}-\frac{1}{61}+\frac{1}{61}-\frac{1}{66}\right)\)

\(=\frac{1}{5}\times\left(\frac{1}{11}-\frac{1}{66}\right)\)

\(=\frac{1}{5}\times\frac{5}{66}=\frac{1}{66}\)

\(\frac{1}{11.16}+\frac{1}{16.21}+\frac{1}{21.26}+...+\frac{1}{61.66}\)

\(=\frac{1}{5}.\left(\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\right)\)

\(=\frac{1}{5}.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)

\(=\frac{1}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)\)

\(=\frac{1}{5}.\frac{5}{66}\)

\(=\frac{1}{66}\)

Bạn dựa vào công thức

a² - n² = (a + n)(a - n)

Đặt \(A=\left(1+\frac{7}{9}\right)\left(1+\frac{7}{20}\right)\left(1+\frac{7}{33}\right)\left(1+\frac{7}{48}\right)+...+\left(1+\frac{7}{2009}\right)\)

\(\Leftrightarrow1+\left(\frac{7}{9}.\frac{7}{20}.\frac{7}{33}.\frac{7}{48}.....\frac{7}{2009}\right)\)

Dãy phân số trên có số phân số là:

(2009 - 9) : 4 + 2 =502

\(\Rightarrow A=1+\left(\frac{7^{502}}{9.20.33.48.....2009}\right)\)

giúp mình với

A=16/9 .27/20 . 40/33 . 55/48 ....2016/2009

   =(16.27.40.55...2016)  /  (9.20.33.48...2009)

   = [(2.8)(3.9)(4.10)(5.11)...(42.48)]   /  [(1.9)(2.10)(3.11)(4.12)...(41.49)]

   =[(2.3.4.5..42)(8.9.10.11..48)]   /   [(1.2.3.4...41)(9.10.11.12...49)]

   =(42.8) / (1.49)

   =336/49

  =48/7

Cậu thông cảm,mk trình bày hơi khó nhìn

a) ( -32 ) . ( -56 ) + 32.44

= 32 . 56 + 32 . 44 

= 32  . ( 56 + 44 )

=  32 . 100

= 3200

b) Làm tương tự như phần a nhé !

Kết bạn nhé !

a) \(\left(-32\right)\cdot\left(-56\right)+32\cdot44\)

\(=32\cdot56+32\cdot44\)

\(=32\cdot\left(56+44\right)\)

\(=32\cdot100\)

\(=3200\)

b) \(\left(-59\right)\cdot\left(-56\right)-59\cdot53\)

\(=59\cdot56-59\cdot53\)

\(=59\cdot\left(56-53\right)\)

\(=59\cdot3\)

\(=177\)

(-32).(-56)+32.44

=32.56+32.44

=32.(56+44)

=32.100=3200

(-59).(-56)-59.53

=59.56-59.53

=59.(56-53)=59.3=177

a) \((-50)+(-10) = -60\)

b) \((-16)+(-14) = -30\)

c) \((-367)+(-33)=-400\)

a) (-12)².x = 56 + 10.13x

=> 144.x = 56 + 130x

=> 144x - 130x = 56

=> 14x = 56

=>x = 56 : 14

=> x = 4

b) 80 - (x² + 5) = 66

=> x² + 5 = 80 - 66

=> x² + 5 = 14

=> x² = 14 - 5

=> x² = 9

=> x² = 3²

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

c) 9 - 25 = (7 - x) - (25 + 7)

=> -16 = (7 - x) - 32

=> 7 - x = -16 + 32

=> 7 - x = 16

=> x = 7 - 16

=> x = -9

d) \(\left(x+5\right)^2=16\)

=> \(\left(x+5\right)^2=4^2\)

=> \(\orbr{\begin{cases}x+5=4\\x+5=-4\end{cases}}\)

=> \(\orbr{\begin{cases}x=-1\\x=-9\end{cases}}\)

a)\(\left(-12\right)^2.x=56+10.13x\)

\(144x=56+130x\)

\(144x-130x=56\)

\(14x=56\)

\(\Rightarrow x=4\)