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Bài 1:
a) \(x^2+10x+26+y^2+2y=(x^2+10x+25)+(y^2+2y+1)\)
..................................................= \(\left(x+5\right)^2+\left(y+1\right)^2\)
b) \(z^2-6z+5-t^2-4t=(z^2-6t+9)-(t^2+4t+4)\)
............................................= \(\left(z-3\right)^2-\left(t+2\right)^2\)
c) \(x^2-2xy+2y^2+2y+1=(x^2-2xy+y^2)+(y^2+2y+1)\)
..................................................= \(\left(x-y\right)^2+\left(y+1\right)^2\)
d) \(4x^2-12x-y^2+2y+8=\left(4x^2-12x+9\right)-\left(y^2-2y+1\right)\)
.................................................= \(\left(2x-3\right)^2-\left(y-1\right)^2\)
Bài 2:
a) \(\left(x+y+4\right)\left(x+y-4\right)=\left(x+y\right)^2-16\)
b) \(\left(x-y+6\right)\left(x+y-6\right)=x^2-\left(y-6\right)^2\)
c) \(\left(y+2z-3\right)\left(y-2z+3\right)=y^2-\left(2z-3\right)^2\)
d) \(\left(x+2y+3z\right)\left(2y+3z-x\right)=\left(2y+3z\right)^2-x^2\)
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Lời giải:
Vì \(x=4; y=8\Rightarrow x^2=16; 2y=16\Rightarrow x^2=2y\Rightarrow x^2-2y=0\).
Do đó:
\(A=(x^2-2y).\frac{x^2(x^2+2y)(x^4+2y^4)(x^8+2y^8)}{x^{16}+2y^{16}}\)
\(=0.\frac{x^2(x^2+2y)(x^4+2y^4)(x^8+2y^8)}{x^{16}+2y^{16}}=0\)
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a, + \(\dfrac{x}{4}\) = \(\dfrac{y}{-5}\) = k ⇒ \(\left\{{}\begin{matrix}x=4k\\y=-5k\end{matrix}\right.\)
Mà -3x + 2y = 55
⇒ -3.4 + 2.-5k = 55
-12k + -10k = 55
(-12 + -10)k = 55
-22k = 55
k = \(\dfrac{55}{22}\) = \(\dfrac{5}{2}\)
+ x = \(\dfrac{5}{2}\).4 = 10
+ y = \(\dfrac{5}{2}\).-5 = \(\dfrac{-25}{2}\)
Vậy x = 10; y = \(\dfrac{-25}{2}\)