For : Compact expression :

Question by Fc Alan Walker

15/12/2017 at 21:53

Compact expression : \(\dfrac{\left(x^2+y^2+z^2\right)\left(a^2+b^2+c^2\right)}{\left(ã+by+cz\right)^2}\)

Nguyễn Hưng Phát 16/12/2017 at 16:35

Lê Quốc Trần Anh that's right.It used many users to swear for me.

I used to remind but it unheard.
Fc Alan Walker selected this answer.
KEITA FC 8C 15/12/2017 at 22:02

Put : \(\dfrac{x}{a}=\dfrac{y}{b}=\dfrac{z}{c}=k\ne0\) then x = ak , y = by , z = ck

So : \(\dfrac{\left(x^2+y^2+z^2\right)\left(a^2+b^2+c^2\right)}{\left(ã+by+cz\right)^2}\)

\(=\dfrac{\left(a^2k^2+b^2k^2+c^2k^2\right)\left(a^2+b^2+c^2\right)}{\left(a^2k+b^2k+c^2k\right)^2}\)

\(=\dfrac{k^2\left(a^2+b^2+c^2\right)^2}{k^2\left(a^2+b^2+c^2\right)^2}\)

\(=1\)
Lê Quốc Trần Anh Coordinator 16/12/2017 at 13:16

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