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प्रश्न
If `x/[3x - y -z] = y/[3y - z -x] = z/[3z -x -y]` and x + y + z ≠ 0 then show that the value of each ratio is equal to 1.
उत्तर
Let `x/[3x - y -z] = y/[3y - z -x] = z/[3z -x -y]` = k
∴ k = `[ x + y + z ]/[( 3x- y -z) + ( 3y - z -x ) + ( 3z - x -y)]` ...(Theorem of equal ratios)
∴ k = `(x + y + z)/(3x - x - x + 3y - y - y + 3z - z - z)`
= `(x + y + z)/(x + y + z)`
∴ k = 1 ...[∵ x + y + z ≠ 0]
∴ Each ratio = 1
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