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a: =>3M+2x^4y^4=x^4y^4
=>3M=-x^4y^4
=>M=-1/3*x^4y^4
b: x^2-2M=3x^2
=>2M=-2x^2
=>M=-x^2
c: =>M=-x^2y^3-3x^2y^3=-4x^2y^3
d: =>M=7x^2y^2-3x^2y^2=4x^2y^2
3x2+4y2=7xy
<=> 3x2-3xy+4y2-4xy=0
<=> 3x(x-y)-4y(x-y)=0
<=> (3x-4y)(x-y)=0
<=> 3x-4y=0 hoặc x-y=0
<=> 3x=4y hoặc x=y
<=> y = \(\frac{3}{4}\)x hoặc x=y
+) y = \(\frac{3}{4}\)x, ta có:
F = \(\frac{4.\frac{3}{4}x+2x}{5.\frac{3}{4}x-7x}+\)\(\frac{3x-2.\frac{3}{4}x}{10.\frac{3}{4}x-4x}\)
F = \(\frac{5x}{-\frac{13}{4}x}+\frac{\frac{3}{2}x}{\frac{7}{2}x}\)
F = \(-\frac{20}{13}+\frac{3}{7}=-\frac{101}{91}\)
+) x = y, ta có:
F = \(\frac{4x+2x}{5x-7x}+\frac{3x-2x}{10x-4x}\)
F = \(\frac{6x}{-2x}+\frac{1x}{6x}=-3+\frac{1}{6}=-\frac{17}{6}\)
Từ \(3x^2+4y^2=7xy\Rightarrow3x^2+4y^2-7xy=0\)
\(\Rightarrow3x^2-4xy-3xy+4y^2=0\)
\(\Rightarrow x\left(3x-4y\right)-y\left(3x-4y\right)=0\)
\(\Rightarrow\left(x-y\right)\left(3x-4y\right)=0\)\(\Rightarrow\left[\begin{matrix}x=y\\x=\frac{4y}{3}\end{matrix}\right.\)
*)Xét \(x=y\) ta có \(F=\frac{4y+2y}{5y-7y}+\frac{3y-2y}{10y-4y}=\frac{6y}{-2y}+\frac{y}{6y}=-3+\frac{1}{6}=-\frac{17}{6}\)
*)Xét \(x=\frac{4y}{3}\) ta có \(F=\frac{4y+2\cdot\frac{4y}{3}}{5y-7\cdot\frac{4y}{3}}+\frac{3\cdot\frac{4y}{3}-2y}{10y-4\cdot\frac{4y}{3}}=\frac{4y+\frac{8y}{3}}{5y-\frac{28y}{3}}+\frac{4y-2y}{10y-\frac{16y}{3}}=\frac{-20}{13}+\frac{3}{7}=\frac{-101}{91}\)
c/\(x^2-2x=2y-xy\)
\(x^2-2x+xy-2y=0\)
\(x\left(x-2\right)+y\left(x-2\right)=0\)
\(\left(x+y\right)\left(x-2\right)=0\)
d/\(x^2+4xy-16+4y^2\)
\(=\left(x^2+4xy+4y^2\right)-16\)
\(=\left(x+2y\right)^2-4^2\)
\(=\left(x+2y-4\right)\left(x+2y+4\right)\)
( 7x + 2y )2 + ( 7x - 2y )2 - 2( 49x2 - 4y2 )
= ( 7x + 2y )2 + ( 7x - 2y )2 - 2( 7x - 2y )( 7x + 2y )
= [ ( 7x + 2y ) - ( 7x - 2y ) ]2
= ( 7x + 2y - 7x + 2y )2
= ( 4y )2 = 16y2
\(=\left(7x+2y\right)^2+\left(7x-2y\right)^2-2\left(7x-2y\right)\left(7x+2y\right)\)
\(=\left(7x+2y-7x+2y\right)^2\)
\(=\left(4y\right)^2=16y^2\)