Question

Cho x : y : z = 3 : 4 : 5 và 2x^2 + 2y ^2 - 3z^ 2 =-100

Answer 1

<=>x/3=y/4=z/5

<=>x²/9=y²/16=z²/25

<=>2x²/18=2y²/32=3z²/75

Theo t/c dãy tỉ số=nhau:

2x²/18=2y²/32=3z²/75=(2x²+2y²-3z²)/(18+32-75)=-100/-25=100/25=4

=>2x²=4.18=72=>x²=36=>x E {-6;6}

2y²=4.32=144=>y²=64=>y E {-8;8}

3z²=4.75=300=>z²=100=>z E {-10;10}

KL:(x;y;z) E {(-6;-8;-10) ; (6;8;10)}
 

Answer 2

ta có: x:y:z=3:4:5\(\Rightarrow\frac{x}{3}=\frac{y}{4}=\frac{z}{5}=k\Rightarrow x=3k;y=4k;z=5k\)

\(2\left(3k\right)^2+2\left(4k\right)^2-3\left(5k\right)^2=-100\)

\(18k^2+32k^2-75k^2=-100\)

\(-25k^2=-100\)

\(k^2=-100:\left(-25\right)\)

\(k^2=4\Rightarrow k=+_{_-}2\)

*vs k=-2, có:x=-2.3=-6

    y=-2.4=-8

z=-2.5=-10

*vs k=2. có:x=2.3=6

y=2.4=8

z=2.5=10

Answer 3

Cảm ơn bạn nhiều nhé Hoàng Phúc :))