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प्रश्न
If a(y + z) = b(z + x) = c(x + y) and out of a, b, c no two of them are equal then show that,
`(y - z)/[a ( b - c )] = ( z - x)/[ b ( c - a)] = ( x - y)/[c ( a - b )]`
उत्तर
Let `a( y + z ) = b( z + x ) = c( x + y) = k`
⇒ `(a( y + z))/(abc) = (b( z + x))/(abc) = (c( x+ y))/(abc)`
`(y + z)/(bc) =(z + x)/(ac) = ( x+ y)/(ab)` = k
`k = (( x + y) - ( z + x))/(ab - ac) = (y - z)/(a(b - c))` ...(1)
`k = (( y + z) - (x + y))/(bc - ab) = (z - x)/(b(c - a))` ...(2)
`k = (( z + x) - (y + z))/(ac - bc) = (x - y)/(c(a - b))` ...(3)
`(therefore a/b = c/d = k = (a - c)/ (b - d))`
`therefore (y - z) /(a(b - c)) = (z - x) /(b(c - a)) = (x - y) /(c(a - b))`
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