Question

[mira jane strauss]

cho x² - y² -z² = 0

c/m ( 5x -3y + 4z) nhân ( 5x - 3y - 4z ) = ( 3x - 5y)²

Answer 1

[kudo shinichi]

\(\left(5x-3y+4z\right)\left(5x-3y-4z\right)=\left(3z-5y\right)^2\)

\(\Leftrightarrow\left(5x-3y\right)^2-\left(4z\right)^2=\left(3x-5y\right)^2\)

\(\Leftrightarrow25x^2-30xy+9y^2-16z^2=9x^2-30xy+25y^2\)

\(\Leftrightarrow16x^2-16y^2-16z^2=0\)

\(\Leftrightarrow16.\left(x^2-y^2-z^2\right)=0\)

Vì \(x^2-y^2-z^2=0\)

\(\Rightarrow\)\(16x^2-16y^2-16z^2=0\)đúng

\(\Rightarrow\)\(\left(5x-3y+4z\right)\left(5x-3y-4z\right)=\left(3z-5y\right)^2\)

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