If x/{b+c}=y/{c+a}=z/{a+b}, then

Correct Answer is : x−yb−a=y−zc−b=z−xa−c

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

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

Algebra and Applications Test 2

Question : 36 of 40

Marks: +1, -0

x/{b+c}=y/{c+a}=z/{a+b},

then

Solution:

x/{b+c}=y/{c+a}=z/{a+b}=k

x = k(b + c)

y = k(c + a)

z = k(a + b)

From the above options

{x-y}/{b-a}={k(b+c)-k(c+a)}/(b-a)

={bk+ck-ck-ak}/{b-a}

={(b-a)k}/{b-a}=k

...(i)
Similearly,

{y-z}/{c-b}=k

...(ii)
and

{z-x}/{a-c}=k

...(iii)
From (i), (ii) and (iii) we get

{x-y}/{b-a}={y-z}/{c-b}={z-x}/{a-c}

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