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2x2-x-6
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\(x-6\sqrt{x-3}+6\text{=}x-3-6\sqrt{x-3}+9\)
\(\text{=}\left(\sqrt{x-3}\right)^2-2.3.\sqrt{x-3}+\left(3\right)^2\)
\(\text{=}\left(\sqrt{x-3}-3\right)^2\)
A = \(x-6\)\(\sqrt{x-3}\) + 6 (đkxd \(x>3\))
A = (\(x\) - 3) - 2.3.\(\sqrt{x-3}\) + 9
A = (\(\sqrt{x-3}\))2 - 2.3.\(\sqrt{x-3}\) + 32
A = (\(\sqrt{x-3}\)- 3)2
\(x^6-y^6\)
\(=\left(x^3-y^3\right)\left(x^3+y^3\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2-xy+y^2\right)\)
x 2 + 5 x – 6 = x 2 – x + 6 x – 6 = ( x 2 – x ) + 6( x – 1)
= x ( x – 1) + 6( x – 1) = ( x – 1)( x + 6)
\(x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2=\left(x^3-y^3\right)\left(x^3+y^3\right)\)
Lời giải:
$x-5\sqrt{x}+6=x-2\sqrt{x}-3\sqrt{x}+6$
$=\sqrt{x}(\sqrt{x}-2)-3(\sqrt{x}-2)$
$=(\sqrt{x}-2)(\sqrt{x}-3)$
\(x-6\sqrt{x}+8\)
\(=x-2\sqrt{x}-4\sqrt{x}+8\)
\(=\sqrt{x}\left(\sqrt{x}-2\right)-4\left(\sqrt{x}-2\right)\)
\(=\left(\sqrt{x}-2\right)\left(\sqrt{x}-4\right)\)
\(x^6-y^6\\ =\left(x^3\right)^2-\left(y^3\right)^2\\ =\left(x^3-y^3\right)\left(x^3+y^3\right)\\ =\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2-xy+y^2\right)\)
\(=x\left(x-6\right)+2\left(x-6\right)=\left(x-6\right)\left(x+2\right)\)
\(2x^2-x-6\)
\(=2x^2-4x+3x-6\)
\(=\left(2x^2-4x\right)+\left(3x-6\right)\)
\(=2x\left(x-2\right)+3\left(x-2\right)\)
\(=\left(x-2\right)\left(2x+3\right)\)
\(=2x^2-2x+3x-6x^2\)
\(=2x\left(x-1\right)+3x\left(1-x\right)\)
\(=2x\left(x-1\right)-3x\left(x-1\right)\)
\(=\left(x-1\right)\left(2x-3x\right)\)
chúc bạn học tốt ^_^ !