Question

Divide 51 into two parts such that their product is 378......................

Answer 1

let one number be 'x'
therefore, other number will be 51-x
(x) (51-x)=378
51x- x^{2} =378
taking 51x -  x^{2} onthe right side we get
 x^{2} - 51x + 378=0
x^{2} -42x - 9x +378 =0
x(x-42) -9(x-42)=0
(x-42)(x-9)=0
x-42=0        x-9=0
 x=42          x=9
therefore x can be 42,9
if one number is 42, then the other numberis 9  

Answer 2

Let one part be y.
Then the other part will be 51-y.
According to the question,
y*(51-y)=378
51y-y²=378
y²-51y+378=0
y²-42y-9y+378=0
y(y-42)-9(y-42)=0
(y-42)(y-9)=0
y=9,42
Therefore we must divide 51 into 42 and 9.