Question

(x+1)(x+3)(x+5)(x+7)=5760 the values of x should be​

Answer 1

Step-by-step explanation:

(x+1)(x+3)(x+5)(x+7) = 5760

In this problem, if u look at the factors on the left,u see that the terms being added are symmetric around 4( in other words 1,7,5&3).

(x+1)(x+7)(x+3)(x+5) = 5760

(x^2+8x+7)(x^2+8x+15) = 5760

Put (t = x^2 + 8x + 11) and we get,

(t-4)(t+4) = 5760

t^2 - 16 = 5760

t^2 = 5776

t = 76 or t = -76

Substitute t =76 in t = x^2 +8x + 11

=>> x^2 +8x +11 = 76

=>> x^2 + 8x -65

=>> x^2 +13x -5x -65

=>> x(x+13) -5 (x+13)

=>> (x+13)=0 or (x-5)=0

=>> x = -13 or x= 5

Therefore values of x= 5 or -13

Hope it will help you