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\(x^6-x^5+3x^4-16x^2+16x-48=0\)

\(\Leftrightarrow\left(x^6-16x^2\right)-\left(x^5-16x\right)+\left(3x^4-48\right)=0\)

\(\Leftrightarrow x^2\left(x^4-16\right)-x\left(x^4-16\right)+3\left(x^4-16\right)=0\)

\(\Leftrightarrow\left(x^4-16\right)\left(x^2-x+3\right)=0\)

\(\Leftrightarrow\left(x^2-4\right)\left(x^2+4\right)\left(x^2-x+3\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x+2\right)\left(x^2+4\right)\left(x^2-x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+2=0\\x^2+4>0\\x^2-x+3=0\left(vonghiem\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)

Vậy.............

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

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

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

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

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

........

1: =(16x^2-8x+1)-y^2

=(4x-1)^2-y^2

=(4x-1-y)(4x-1+y)

2: =(x^2-2xy+y^2)-z^2

=(x-y)^2-z^2

=(x-y-z)(x-y+z)

3: =(x^2+4xy+4y^2)-16

=(x+2y)^2-4^2

=(x+2y-4)(x+2y+4)

4: =(x^2-4xy+4y^2)-16

=(x-2y)^2-4^2

=(x-2y-4)(x-2y+4)