Maths questions
Maths questions Q.1. How many ordered pairs of integers satisfy (x,y) the equation 1/x+1/y=1/12 Lets try and solve it using good old school algebra. 1 x + 1 y = 1 12 1 x + 1 y = 1 12 Or, ( x + y ) x y = 1 12 ( x + y ) x y = 1 12 Or, 12 x + 12 y − x y = 0 12 x + 12 y − x y = 0 Or, 12 x − x y + 12 y − 144 + 144 = 0 12 x − x y + 12 y − 144 + 144 = 0 Or, x ( 12 − y ) − 12 ( 12 − y ) + 144 = 0 x ( 12 − y ) − 12 ( 12 − y ) + 144 = 0 Or, ( x − 12 ) ( 12 − y ) = ( − 144 ) ( x − 12 ) ( 12 − y ) = ( − 144 ) Or, ( x − 12 ) ( y − 12 ) = 144 ( x − 12 ) ( y − 12 ) = 144 … Eqn1 Now, 144 = ( 2 ) 4 × ( 3 ) 2 144 = ( 2 ) 4 × ( 3 ) 2 So, it has ( 1 + 4 ) × ( 1 + 2 ) ( 1 + 4 ) × ( 1 + 2 ) = 15 factors. Factors : 1, 2, 3, 4, 6,……., 36, 48, 72, 144 Thus it can be expressed as product of 2 factors in (...