Question

Find three positive consecutive integers whose product is 16 times the sum

Answer 1

Solution:-

let ,
three positive consecutive integers :-

x , x-1 , x+1

acourding to quetion:-

x(x-1)(x+1) = 16(x+x-1+x)

$x(x - 1)(x + 1) = 16(x + x - 1 + x + 1) \\ x( {x}^{2} - 1) = 16(3x) \\ x( {x}^{2} - 1) = 48x \\ {x}^{2} - 1 = 48 \\ {x}^{2} = 48 + 1 \\ {x}^{2} = 49 \\ x = \sqrt{49} \\ x = 7 \\ x - 1 = 7 - 1 = 6 \\ x + 1 = 7 + 1 = 8 \\ the \: numbers \: are = 6 > 7 > 8$