Question

Bài 1. Viết các đa thức dưới đây thành tích

a,y^4-14y^2+49

b,1/4-x^2

c,x^4-16

d,x^2-9

Bài 2. Rút gọn rồi thay x,y

a, 4x^2-2x+1/4. (x=3,x=19)

b,25a^2+10/3a+1/9. (a=9,a=2009)

c,4x^2+y^2-4x. (2x-y=4)

Giúp mk với ạ !

 

Answer 1

Answer 2

a. y⁴ - 14y² + 49

Gọi y² là t, ta có:

t² - 14t + 49

<=> t² - 14t + 7²

<=> (t - 7)²

Thay x² = t

<=> (x² - 7)²

b. \(\dfrac{1}{4}-x^2\)

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

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

c. x⁴ - 16

<=> (x²)² - 4²

<=> (x² - 4)(x² + 4)

d. x² - 9

<=> x² - 3²

<=> (x - 3)(x + 3)

 

Answer 3

Bài 1: 

a: \(y^2-14y^2+49=\left(y-7\right)^2\)

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

c: \(x^4-16=\left(x-2\right)\left(x+2\right)\left(x^2+4\right)\)

d: \(x^2-9=\left(x-3\right)\left(x+3\right)\)

Answer 4

a, y⁴-14y²+49= (y²)²- 2.y².7+ 7²= (y²- 7)²

b, \(\dfrac{1}{4}-x^2=\left(\dfrac{1}{2}\right)^2-x^2=\left(\dfrac{1}{2}-x\right).\left(\dfrac{1}{2}+x\right)\)

c, x⁴- 16= (x²)² - 4²= (x²-4).(x²+4)

Bài 2

a, \(4x^2-2x+\dfrac{1}{4}=\left(2x\right)^2-2.2x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2=\left(2x-\dfrac{1}{2}\right)^2\)

+) x=3 ta có: \(\left(2.3-\dfrac{1}{2}\right)^2=\left(\dfrac{11}{2}\right)^2=\dfrac{121}{4}\)

+) x= 19 ta có: \(\left(2.19-\dfrac{1}{2}\right)^2=\left(\dfrac{75}{2}\right)^2=\dfrac{5625}{4}\)

b, \(25a^2+\dfrac{10}{3}a+\dfrac{1}{9}=\left(5a\right)^2+2.5a.\dfrac{1}{3}+\left(\dfrac{1}{3}\right)^2=\left(5a+\dfrac{1}{3}\right)^2\)

+) a=9 ta có: \(\left(5.9+\dfrac{1}{3}\right)^2=\left(\dfrac{136}{3}\right)^2\)

+) a=2009 ta có: \(\left(5.2009+\dfrac{1}{3}\right)^2=\left(\dfrac{30136}{3}\right)^2\)

Hoctot

Answer 5

Bài 2:

a. 4x² - 2x + \(\dfrac{1}{4}\)

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

<=> \(\left(2x-\dfrac{1}{2}\right)^2\)

Thay x = 3 vào PT:

\(\left(6-\dfrac{1}{2}\right)^2\)

= 5,5²

= 30,25

Thay x = 19 vào PT:

\(\left(38-\dfrac{1}{2}\right)^2\)

= 37,5²

= \(\dfrac{5625}{4}\)

b. 25a² + \(\dfrac{10}{3a}\) + \(\dfrac{1}{9}\)

<=> \(\left(5a+\dfrac{1}{3}\right)^2\)

Thay a = 9 vào PT:

\(\left(45+\dfrac{1}{3}\right)^2\)

= \(\left(\dfrac{136}{3}\right)^2\)

= \(\dfrac{18496}{9}\)

Thay x = 2009 vào PT:

\(\left(10045+\dfrac{1}{3}\right)^2\)

= \(\left(\dfrac{30136}{3}\right)^2\)

= 100908721,8

c. 4x² + y² - 4x

<=> 4x² - 4x + y²

Mik cảm thấy đề câu C có phần sai sai, bạn xem lại rồi nhắc mik