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(x2n+xnyn+y2n)(xn−yn)(x3n+y3n)=[(xn)2+xnyn+(yn)2](xn−yn)(x3n+y3n)=(x3n−y3n)(x3n+y3n)=x6n−y6n
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bài 2 :
x3+7y=y3+7x
x3-y3-7x+7x=0
(x-y)(x2+xy+y2)-7(x-y)=0
(x-y)(x2+xy+y2-7)=0
\(\left\{{}\begin{matrix}x-y=0\Rightarrow x=y\left(loại\right)\\x^{2^{ }}+xy+y^2-7=0\end{matrix}\right.\)
x2+xy+y2=7 (*)
Giải pt (*) ta đc hai nghiệm phan biệt:\(\left[{}\begin{matrix}x=1va,y=2\\x=2va,y=1\end{matrix}\right.\)
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\(b,\left(5x-7y^2\right).\left(5x+7y^2\right)=\left(25x^2-49y^4\right)\)
\(c,\left(5x-7y\right)^2.\left(5x+7y\right)^2=\left(25x^2-70xy+49x^2\right).\left(25x^2+70xy+49x^2\right)\)\(d,\left(\frac{1}{3}x+5y\right).\left(5y-\frac{1}{3}x\right)=25y^2-\frac{1}{9}x^2\) học tốt nhaa) (2x-y)2 = (2x)2 - 2.2x.y + y2 =4x2-4xy+y2
b)(5x-7y2).(5x+7y2) = (5x)2 - (7y2) 2 =25x2 - 49y4
câu c,d mk ko bít làm
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đừng sủa lắm , không biết mỏi mồm à
a,\(\left(3x-2y\right)^2-\left(5x+7y\right)^2-14y^2\)
\(=9x^2+4y^2-12xy-25x^2-49y^2-70xy-14y^2\)
\(=-16x^2-59y^2-82xy\)
b,\(-\left(4x-\frac{3}{2}\right)^2+\left(3-2x\right)^2-\frac{1}{4}\)
\(=-16x^2+12x-\frac{9}{4}+9-12x+4x^2-\frac{1}{4}\)
\(=-12x^2-\frac{5}{2}+9=\frac{13}{2}-12x^2\)
c,\(\left(2x+1\right)^2-2\left(2x+1\right).\left(7+3x\right)+\left(7+3x\right)^2\)
\(=\left(2x+1-7-3x\right)^2=\left(-6-x\right)^2=36+12x+x^2\)
d, \(\left(5-3x\right)^2+2\left(5-3x\right)\left(7+3x\right)+\left(7+3x\right)^2\)
\(=\left(5-3x+7+3x\right)^2=12^2=144\)