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Variation
For proportional (µ) sign, we use '@' sign for input.
 
1. Find value of variation using given value
Variation
Given
Find
  1. `X prop Y` and `X=4,Y=2`. Find `X=18,Y=?`
  2. `X prop 1/Y^3` and `X=16,Y=1/2`. Find `X=54,Y=?`
  3. `X prop Y^3/Z` and `X=8,Y=4,Z=3`. Find `X=?,Y=6,Z=4`
  4. `X prop YZ` and `X=8,Y=4,Z=3`. Find `X=?,Y=6,Z=4`
  5. `X prop Y^3Z` and `X=8,Y=4,Z=3`. Find `X=?,Y=6,Z=4`

2. Prove results for given variation
Variation
Prove that
Constant
  1. If `X prop Y` then prove that `X^3+Y^3 prop X^2Y-XY^2`
  2. If `X prop Y` then prove that `X^2+Y^2+XY prop X^2-Y^2`
  3. If `X prop Y, Y prop Z` then prove that `X^3+Y^3+Z^3 prop XYZ`
  4. If `Y prop Z, X prop Y` then prove that `X^3+Y^3+Z^3 prop XYZ`
  5. If `5X-7Y prop 6X+3Y` then prove that `X prop Y `
  6. If `5X+2Y prop 3X-7Y` then prove that `X prop Y `
  7. If `9X-3Y prop 4X+5Y` then prove that `X prop Y `
  8. If `2X^2-3Y^2 prop 4X^2+5Y^2` then prove that `X prop Y `
  9. If `4X^3+5Y^3 prop 2X^3-9Y^3` then prove that `X prop Y `
  10. If `X^2+9Y^2 prop XY` then prove that `X prop Y `
  11. If `4X^2+9Y^2 prop XY` then prove that `X^2+Y^2 prop XY `
 
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