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# If X 3 X − Y − Z = Y 3 Y − Z − X = Z 3 Z − X − Y and X + Y + Z ≠ 0 Then Show that the Value of Each Ratio is Equal to 1. - Algebra

Sum

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.

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#### Solution

x/[3x - y -z] = y/[3y - z -x] = z/[3z -x -y] = [ x + y + z ]/[( 3x- y -z) + ( 3y - z -x ) + ( 3z - x -y)]                                                            ( Theorem of equal ratios)
⇒ x/[3x - y -z] = y/[3y - z -x] = z/[3z -x -y] =[ x + y + z ]/[ x + y + z ]

⇒x/[3x - y -z] = y/[3y - z -x] = z/[3z -x -y] = 1

Concept: Theorem on Equal Ratios
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#### APPEARS IN

Balbharati Mathematics 1 Algebra 9th Standard Maharashtra State Board
Chapter 4 Ratio and Proportion
Practice Set 4.4 | Q 4.2 | Page 73
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