Question

divide 57 into two parts whose product is 680.

Answer 1

Hi ,

57 is divided into two parts.

Let one part = x

Second part = 57 - x

According to the given problem ,

Product of the two numbers = 680

x ( 57 - x ) = 680

57x - x^2 = 680

x^2 - 57x +680 = 0

Spilt the middle term

x^2 -40x -17x + 680 = 0

x ( x - 40 ) - 17 ( x - 40 ) = 0

( x - 40 )( x - 17 ) = 0

Therefore ,

x - 40 = 0 or x - 17 = 0

x = 40 or x = 17

Required two parts are

i) One part = x = 40

Second part = 57 - x = 57 - 40 = 17

Or

One part = x = 17

Second part = 57 - 17 = 40

I hope this helps you.

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Answer 2

Let one part be x

Second part be 57- x

(x) (57-x) = 680

57x - x² =680

x² -57x +680 =0

x² -40 x -17x +680=0

x(x-40) -17(x-40) =0

(x-40)(x-17) =0

x-40 =0 or x-17=0

x=40. or x= 17

57-x = 57-40 =17

or

57-x = 57 -17 =40

This is the answer.

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Hope this helps you.