Question

[Nhok Ngịch Ngợm]

cho x²-y²-z²=0

chúng minh : (5x-3y+4z)(5x-3y-4z)=(3x-5y)²

Answer 1

[Bellion]

            Bài làm :

Ta có:

\(x^2-y^2-z^2=0\)

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

\(\Leftrightarrow25x^2-9x^2+9y^2-25y^2-16z^2+30xy-30xy=0\)

\(\Leftrightarrow\left[\left(25x^2-30xy+9y^2\right)-16z^2\right]-\left(9x^2-30xy+25y^2\right)=0\)

\(\Leftrightarrow\left(5x-3y\right)^2-16z^2=\left(3x-5y\right)^2\)

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

=> Điều phải chứng minh

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