Question

if

(x+3)(x+4)(x+6)(x+7)=1120
solve for value of x

Answer 1

1/x = 1/(7 + 4√3) 
=(7 - 4√3)/(7 + 4√3)(7 -4√3)
=(7 -4√3)/(7² -4√3²)
=(7 - 4√3)/(49 - 48)
=( 7 - 4√3)

hence, x + 1/x = (7 + 4√3) + (7 - 4√3) = 14 

x³ + 1/x³ = (x + 1/x)³ -3(x + 1/x )
= ( 14)³ - 3(14)
= 14 × 193 
= 2702

Answer 2

$( {x}^{2} + 4x + 3x + 12) \times (x + 6) \times (x + 7) = 1120 \\x = - 11 \\ x = 1$