Question

Giải phương trình:

b) \(\dfrac{7}{2}-\left(\dfrac{x}{5}-\dfrac{1}{4}\right)=\dfrac{9}{2}\)

c) (x+2) . (x-5). (x-6) (x+3) = 180

d) \(x-\dfrac{\dfrac{x}{2}-\dfrac{3+x}{4}}{2}=\dfrac{2x-\dfrac{10-7x}{3}}{2}-x-1\)

e) \(\left(\dfrac{1}{1.101}+\dfrac{1}{2.102}+........+\dfrac{1}{10.110}\right).\left(x-3\right)=\dfrac{1}{1.11}+\dfrac{1}{2.12}+.......+\dfrac{1}{100.110}\)

Answer 1

b) \(\dfrac{7}{2}-\left(\dfrac{x}{5}-\dfrac{1}{4}\right)=\dfrac{9}{2}\)

<=> \(\dfrac{7}{2}-\dfrac{x}{5}+\dfrac{1}{4}=\dfrac{9}{2}\)

<=> \(\dfrac{15}{4}-\dfrac{x}{5}-\dfrac{9}{2}=0\)

<=> \(\dfrac{x}{5}=\dfrac{5}{4}\)

<=> x = 6,25

Vậy,...

c) ( x + 2)( x + 3)( x - 5)( x - 6) = 180

<=> ( x + 2)( x - 5)( x + 3)( x - 6) = 180

<=> ( x² - 3x - 10 )( x² - 3x - 18 ) = 180

Đặt : x² - 3x - 14 = a , ta có :

( a + 4)( a - 4) = 180

<=> a² - 16 - 180 = 0

<=> a² - 196 = 0

<=> ( a - 14)( a + 14 ) = 0

<=> a = 14 hoặc a = -14

* Với , a = 14 , ta có :

x² - 3x - 14 = 14

<=> x² - 3x - 28 = 0

<=> x² - 7x + 4x - 28 = 0

<=> x( x - 7) + 4( x - 7) = 0

<=> ( x + 4)( x - 7) = 0

<=> x = -4 hoặc : x = 7

* Với : a = -14 , ta có :

x² - 3x - 14 = -14

<=> x( x - 3) = 0

<=> x = 0 hoặc : x = 3

Vậy,...