Question

if x+y ∝z , when y is constant and z+x ∝y , when x is constant, then prove that, x+y+z ∝yz , where x, y, z ere variable

Answer 1

∵ x+y ∝ z 
∴ x+y = mz ( where m is a constant.)
Adding z on both sides, 
   x+y+z=mz+z=(m+1)z(when y is contant.)
 ⇒  x+y+z ∝ z [∵ (m+1) is a constant.] .......(1)

∵ z+x ∝ y
∴ z+x = ny ( where n is a constant.)
Adding y on both sides,
   x+y+z = ny +y = (n+1)y (when x is a constant.)
 ⇒x+y+z ∝ y[∵ (n+1) is a constant.]..............(2)

From (1) and (2), using the theorem of joint variation, we get,
 x+y+z ∝ yz when both x and y vary.                        (Proved.)
 

Answer 2

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