Question

[Lucy cute]

Find the value of expresssion x² + y² + z², if x+y+z = 5 and \(\dfrac{1}{x}\) + \(\dfrac{1}{y}\) + \(\dfrac{1}{z}\)= 0

Answer 1

[Akai Haruma]

Lời giải:

$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0$

$\Rightarrow xy+yz+xz=0$

Khi đó:

$x^2+y^2+z^2=(x+y+z)^2-2(xy+yz+xz)=5^2-2.0=25$