Question

[Tran Thi Kim Phung]

Cho x:y:z=3:4:5 và 2X²+2Y²-3Z²=-100

Khi đó (x+y+z)²=...

Answer 1

[Hoàng Phúc]

x:y:z=3:4:5

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

=>x²/9=y²/16=z²/25

=>2x²/18=2y²/32=3z²/75

Theo t/c dãy tỉ số=nahu:

\(\frac{2x^2}{18}=\frac{2y^2}{32}=\frac{3z^2}{75}=\frac{2x^2+2y^2-3z^2}{18+32-75}=-\frac{100}{-25}=\frac{100}{25}=4\)

=>2x²=4.18=72=>x²=36=>x E {-6;6}

2y²=4.32=128=>y²=64=>y E {-8;8}

3z²=4.75=300=>z²=100=>z E {-10;10}

+)(x+y+z)²=(6+8+10)²=576

+)(x+y+z)²=[(-6)+(-8)+(-10)]²=(-24)²=576

Vậy (x+y+z)²=576