Maharashtra State BoardSSC (English Medium) 9th Standard
Advertisement Remove all ads

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.

Advertisement Remove all ads

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
  Is there an error in this question or solution?
Advertisement Remove all ads

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
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×