Question

if z=(x+y)+(x+y)$[y/x] then prove that x[d^2z/dx^2-d^2z/dydx]=y[d^2z/dy^2-d^2z/dxdy]​

Answer 1

Aɴsᴡᴇʀ࿐

Let Z be the number

Z = 13x + 11 where x is the quotient when Z is divided by 13

Z = 17y + 9 where y is the quotient when Z is divided by 17

13x + 11 = 17y + 9

13x + 2 = 17y since x and y are quotients they should be whole numbers . Since y has to be a whole number the left hand side should be multiple of 17

The least possible value of x satisfying the condition is 9 and y will be 7

The answer is 13*9 + 11 = 128 or it is 17*7 + 9 = 128

This is the least number possible. There will be multiple answers and will increase in multiples 17*13 = 221 like 349 , 570, etc.

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