Question

If (x+1)(x+3)(x+5)(x+7)=5760, find the real values of x.
A. 5,13
B. -5,13
C. -5,-13
D. 5,-13

Answer 1

If (x+1)(x+3)(x+5)(x+7)=5760, find the real values of x.

Solution,

Option D is the right answer,

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

6*8*10*12=5760

5760=5760

(-13+1)(-13+3)(-13+5)(-13+7)=5760

-12*-10*-8*-6=5760

5760=5760

(x+1)(x+3)(x+5)(x+7)=5760  ---->A

Above equation has symmetry that is around 4 (highest power 4). so put x=b-4 in eq A

(b−3)(b−1)(b+1)(b+3)=5760  --->B

(b^2-9)(b^2-1)=5760 --->C

Now substitute z+5 in equation C in (b^2)

(z+5-9)(z+5-1)=5760

(z-4)(z+4)=5760

z^2-16=5760

z^2=5776

taking root on both sides,

z=+76, z=-76

b^2=z+5=76+5

b^2=81

(b^2-9)(b^2-1)=5760 --->C

Put b^2=81 in eq C,

(81-9)(81-1)=5760

72*80=5760

5760=5760

Answer 2

option D is the correct answer.