If-ax-by-cz-0-and-a-2-x-b-2-y-c-2-z-0-Find-the-ratio-x-y-z-

Question Number 7612 by Tawakalitu. last updated on 06/Sep/16

I f a x + b y + c z = 0,

a n d, a^{2} x + b^{2} y + c^{2} z = 0

F i n d t h e r a t i o x : y : z

Commented by Rasheed Soomro last updated on 06/Sep/16

a x + b y + c z = 0 \dots \dots \dots \dots \dots . . (i)

a^{2} x + b^{2} y + c^{2} z = 0 \dots \dots \dots \dots . (i i)

x = \frac{- b y - c z}{a}

x = \frac{- b^{2} y - c^{2} z}{a^{2}}

\frac{- b y - c z}{a} = \frac{- b^{2} y - c^{2} z}{a^{2}}

- a b y - a c z = - b^{2} y - c^{2} z

b^{2} y - a b y = - c^{2} z + a c z

b (b - a) y = c (a - c) z

\frac{y}{z} = \frac{c (a - c)}{b (b - a)}

y : z = c (a - c) : b (b - a) \dots \dots \dots . (i i i)

A g a i n f r o m (i) & (i i)

z = \frac{- a x - b y}{c}

z = \frac{- a^{2} x - b^{2} y}{c^{2}}

\frac{- a x - b y}{c} = \frac{- a^{2} x - b^{2} y}{c^{2}}

- a c x - b c y = - a^{2} x - b^{2} y

a^{2} x - a c x = b c y - b^{2} y

a (a - c) x = b (c - b) y

\frac{x}{y} = \frac{b (c - b)}{a (a - c)}

x : y = b (c - b) : a (a - c) \dots \dots \dots \dots \dots \dots . (i v)

B y c o m b i n i n g (i v) & (i i i)

(\begin{matrix} x & : & y & : & z \\ b (c - b) & : & a (a - c) \\ c (a - c) & : & b (b - a) \\ b c (c - b) & : & c a (a - c) & : & a b (b - a) \end{matrix})

Commented by Tawakalitu. last updated on 06/Sep/16

W o w, t h a n k y o u s o m u c h s i r .

Commented by Tawakalitu. last updated on 06/Sep/16

T h a n k s s o m u c h s i r . G o d b l e s s y o u

Answered by Yozzia last updated on 06/Sep/16

A n s w e r i n c o m m e n t s .

Facebook Tweet Pin