(toán 8)chứng minh 2 đa thức bằng nhau

Q

quynhphamdq

[TEX]a)(5x-3y+4z)(5x-3y-4z)[/TEX]
[TEX]=(5x-3y )^2-16z^2[/TEX]
[TEX]=25x^2-30xy+9y^2-16z^2(*)[/TEX]
Vì [TEX]x^2=y^2 + z^2[/TEX]
\Rightarrow [TEX]z^2= x^2- y^2[/TEX]
\Rightarrow[TEX] (*)=25x^2-30xy+9y^2-16.(x^2- y^2)=(3x-5y)^2 [/TEX](đpcm)
 
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I

iceghost

$x^2=y^2+z^2 \\
\implies x^2-y^2=z^2 \\
\implies 16x^2-16y^2=16z^2$

$(5x-3y+4z)(5x-3y-4z) \\
= (5x-3y)^2-16z^2 \\
= 25x^2-30xy+9y^2-(16x^2-16y^2) \\
= 9x^2 - 30xy + 25y^2 \\
= (3x-5y)^2$
 
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