@yurenchu

(x+1)(x+2)(x+3)(x+4) = 120

120 = 2*3*4*5 = (-5)*(-4)*(-3)*(-2)
hence upon inspection, we easily see that x = 1 and x = -6 are solutions to the equation. But there are two more solutions.

... Substitute u = (x + 2.5):
(u - 1.5)(u - 0.5)(u + 0.5)(u + 1.5) = 120
(u - 1.5)(u + 1.5)*(u - 0.5)(u + 0.5) = 120
(u² - 1.5²)*(u² - 0.5²) = 120
(u² - 2.25)*(u² - 0.25) = 120
... Substitute t = (u² - 1.25):
(t - 1)(t + 1) = 120
t² - 1 = 120
t² = 121
t = 11  OR  t = -11

t = 11:
(u² - 1.25) = 11
u² = 12.25
u = 3.5  OR  u = -3.5
x + 2.5 = 3.5  OR  x + 2.5 = -3.5
x = 1  OR  x = -6

t = -11:
(u² - 1.25) = -11
u² = -9.75 = -39/4
u = (i/2)√39  OR  u = -(i/2)√39
x + 2.5 = (i/2)√39  OR  x + 2.5 = -(i/2)√39
x = -5/2 + (i/2)√39  OR  x = -5/2 - (i/2)√39
x = (-5 + i√39)/2  OR  x = (-5 - i√39)/2

==> Solution: x = 1  OR  x = -6  OR  x = (-5 + i√39)/2  OR  x = (-5 - i√39)/2

@21gamer50

substitute 
x = a - 2.5 
2.5 is avg of 1,2,3,4

then, substitute a^2 = u + 1.25
1.25 is also avg 
Ez..

@johnlister

Wow! That makes a mountain out of a molehill!

I would hope that someone entering Harvard would say, the product is of 4 consecutive numbers. 120 = 5! so the four numbers are 2, 3, 4, 5. Therefore x = 1. 

I suspect that going into that level of detail would not impress the interviewer. 

PS: I have my own interview failure question from 50 years ago at Cambridge (UK) involving a cube of resistors and finding the overall resistance across the corners. Still haven't worked that one out yet.

@norbertduchting6217

After some meditation you see that the equation is equivalent to (x^2 +5x +5)^2 = 121. The rest is easy.

@tom-kz9pb

I could see "X=1" in just a glance.  Does Harvard specify that it wants ALL the possible solutions, or just a solution that works?

@nasifajahan4688

Sir, you are great😃. Go ahead❤

@nelsonmontenegro8167

Muchas vueltas. Sí por simple inspección o por descomposición de factores.       X=1.  Entonces. (1+1) (1+2)(1+3)(1+4)= 120.

@max0ua

x^2 + 5x + 5 = u => (u - 1)(u + 1) = 120

@TheRider995.

Simple method, LHS मे x का मान 1रखने पर = 120 
So LHS=RHS.

@daliaghosh3980

120=5!=(4+1)(3+1)(2+1)(1+1)
So x=1  ans.

@SuperAnangs

In a blink  x is solved x=1

@daysongrohs8502

How are so many people over explaining over thinking and getting the wrong number for x 😂 I literally glanced at it and could see x=1

@CaptainDangeax

2×3×4×5=120. X=1 is a solution

@ngocdo5687

(x+1)(x+2)(x+3)(x+4)
          = 120.
* 120 = 10 x 12 
         = 2x5 x 3x4
         = 2 x 3 x 4 x 5.
= (1+1)(1+2)(1+3)(1+4)
** x = 1./.

@ЭдуардПлоткин-р3л

Если бы в Гарварде давали такие задания,туда поступил бы любой желающий.Не нужно врать!

@RazaArcX

Bro geometry please 🙏🙏

@thomasrusterholz8179

why repeat the problem? we can all see it

@LarryWashington-t2m

Where is the practical use?

@哲-h7r

120を素因数分解するだけだよ！
120＝2exp3×3×5＝2×3×4×5

@ABM100

x=1 e x=-6