Question

Tìm x biết.
a) 4x^2 - 49 = 0 b) x^2 + 36 = 12x
c) 1/16x^2 - x + 4 = 0 d) x^3 -3√3x2 + 9x - 3√3 = 0
e) (x - 2)^2 - 16 = 0 f) x^2 - 5x - 14 = 0
g) 8x(x - 3) + x - 3 = 0

Answer 1

a, 4x² - 49 = 0

⇔⇔ (2x)² - 7² = 0

⇔⇔ (2x - 7)(2x + 7) = 0

⇔{2x−7=02x+7=0⇔⎧⎪ ⎪⎨⎪ ⎪⎩x=72x=−72⇔{2x−7=02x+7=0⇔{x=72x=−72

b, x² + 36 = 12x

⇔⇔ x² + 36 - 12x = 0

⇔⇔ x² - 2.x.6 + 6² = 0

⇔⇔ (x - 6)² = 0

⇔⇔ x = 6

Answer 2

e, (x - 2)² - 16 = 0

⇔⇔ (x - 2)² - 4² = 0

⇔⇔ (x - 2 - 4)(x - 2 + 4) = 0

⇔⇔ (x - 6)(x + 2) = 0

⇔{x−6=0x+2=0⇔{x=6x=−2⇔{x−6=0x+2=0⇔{x=6x=−2

f, x² - 5x -14 = 0

⇔⇔ x² + 2x - 7x -14 = 0

⇔⇔ x(x + 2) - 7(x + 2) = 0

⇔⇔ (x + 2)(x - 7) = 0

⇔{x+2=0x−7=0⇔{x=−2x=7

Answer 3

a,\(4x^2-49=0\)

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

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

\(\Leftrightarrow\orbr{\begin{cases}2x-7=0\\2x+7=0\end{cases}\Leftrightarrow\orbr{\begin{cases}2x=7\\2x=-7\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{7}{2}\\x=-\frac{7}{2}\end{cases}}}\)

b.\(x^2+36=12x\)

\(\Leftrightarrow x^2-12x+36=0\)

\(\Leftrightarrow\left(x-6\right)^2=0\)

\(\Leftrightarrow x-6=0\Leftrightarrow x=6\)

c.\(\frac{1}{16x^2}-x+4=0\)

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

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

........

Answer 4

Trả lời:

a, 4x² - 49 = 0

<=> ( 2x - 7 ) ( 2x + 7 ) = 0

<=> 2x - 7 = 0 hoặc 2x + 7 = 0

<=> 2x = 7 hoặc 2x = - 7

<=> x = 7/2 hoặc x = - 7/2

Vậy S = { 7/2; - 7/2 }

b, x² + 36 = 12

<=> x² + 36 - 12x = 0

<=> x² - 2 . x . 6 + 6² = 0

<=> ( x - 6 )² = 0

<=> x - 6 = 0 

<=> x = 6 

Vậy S = { 6 }

c, \(\frac{1}{16}x^2-x+4=0\)

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

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

\(\Leftrightarrow\frac{1}{4}x-2=0\)

\(\Leftrightarrow\frac{1}{4}x=2\)

\(\Leftrightarrow x=8\)

Vậy S = { 8 }

e, ( x - 2 )² - 16 = 0

<=> ( x - 2 - 4 ) ( x - 2 + 4 ) = 0

<=> ( x- 6 ) ( x + 2 ) = 0

<=> x - 6 = 0 hoặc x + 2 = 0

<=> x = 6 hoặc x = - 2

Vậy S = { 6; - 2 }

f, x² - 5x - 14 = 90

<=> x² - 7x + 2x - 14 = 0

<=> ( x² - 7x ) + ( 2x - 14 ) = 0

<=> x ( x - 7 ) + 2 ( x - 7 ) = 0 

<=> ( x + 2 ) ( x - 7 ) = 0

<=> x + 2 = 0 hoặc x - 7 = 0

<=> x = - 2  hoặc x = 7

Vậy S = { 2; - 7 }

g, 8x ( x - 3 ) + x - 3 = 0

<=> 8x ( x - 3 ) + ( x - 3 ) = 0

<=> ( x - 3 ) ( 8x + 1 ) = 0

<=> x - 3 = 0 hoặc 8x + 1 = 0

<=> x = 3 hoặc x = - 1/8

Vậy S = { 3; - 1/8 }