Câu hỏi của Quanh Phan

Question

Rút gọn các biểu thức sau: $\dfrac{(x+5)^2+(x-5)^2}{x^2+25}$=

$(x+3)(x^2-3x+9)-(54+x^3)$=

\((2x+y)^2-(y+3...

Aki Tsuki · Accepted Answer

$x^2+6x+9=\left(x+3\right)^2$

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

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$x^3+12x^2+48x+64=\left(x+4\right)^3$Câu trả lời: $x^2+6x+9=\left(x+3\right)^2$

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

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$x^3+12x^2+48x+64=\left(x+4\right)^3$

Nháy >.< · Answer

1) $\dfrac{\left(x+5\right)^2+\left(x-5\right)^2}{x^2+25}$

$=\dfrac{x^2+10x+25+x^2-10x+25}{x^2+25}$

$=\dfrac{2x^2+50}{x^2+25}$

$=\dfrac{2\left(x^2+25\right)}{x^2+25}=2$

2) $\left(x+3\right)\left(x^2-3x+9\right)-\left(54+x^3\right)$

$=x^3+3^3-54-x^3$

$=27-54=-27$

3) $\left(2x+y\right)^2-\left(y+3x\right)^2$

$=4x^2+4xy+y^2-y^2-6xy-9x^2$

$=-5x^2-2xy$

4) $\left(2x+1\right)^3-\left(2x-1\right)^3-24x^2$

$=8x^3+12x^2+6x+1-8x^3+12x^2-6x+1-24x^2$

$=2$Câu trả lời: 1) $\dfrac{\left(x+5\right)^2+\left(x-5\right)^2}{x^2+25}$