BeMath-Given-2x-2x-6-5y-5y-25-4z-4z-16-and-xy-yz-xz-188-Find-the-solution-

Question Number 108769 by bemath last updated on 19/Aug/20

\frac{\iddots B e M a t h ⋱}{★}

G i v e n \frac{2 x}{2 x + 6} = \frac{5 y}{5 y + 25} = \frac{4 z}{4 z + 16}

a n d x y + y z + x z = 188 . F i n d t h e

s o l u t i o n

Answered by john santu last updated on 19/Aug/20

\frac{⊸ J S ⊸}{♡}

\Rightarrow \frac{x}{x + 3} = \frac{y}{y + 5} = \frac{z}{z + 4}

\Rightarrow \frac{x + 3}{x} = \frac{y + 5}{y} = \frac{z + 4}{z}

\Rightarrow \frac{3}{x} = \frac{5}{y} = \frac{4}{z} \to {\begin{cases} y = 5 b \\ x = 3 b \\ z = 4 b \end{cases}

\Rightarrow 15 b^{2} + 12 b^{2} + 20 b^{2} = 188

\Rightarrow 47 b^{2} = 188; \to {\begin{cases} b = 2 \\ b = - 2 \end{cases}

c a s e (1) b = 2 \to {\begin{cases} x = 6 \\ y = 10 \\ z = 8 \end{cases}

c a s e (2) b = - 2 \to {\begin{cases} x = - 6 \\ y = - 10 \\ z = - 8 \end{cases}

Commented by bemath last updated on 19/Aug/20

j o o s s

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