Question

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

Solve this question ​

Answer 1

Answer:

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

⟹(x+1)(x+4)(x+2)(x+3)=120

⟹(x2+5x+4)(x2+5x+6)=120

Letx2+5x=y

(y+4)(y+6)=120

⟹y2+10y+24=120

⟹y2+10y−96=0

⟹y2+16x−6x−96=0

⟹y(y+16)−6(y+16)=0

(y+16)(y−6)=0

⟹y=−16andy=6

∴x2+5x=6⟹x2+5x−6=0

x2+6x−x−6=0

x(x+6)−1(x+6)=0

(x+6)(x−1)=0

⟹x=−6andx=1real solutions

also

x2+5x=−16⟹x2+5x+16=0

x=−5±25−64−−−−−−√2

⟹x=−5±−39−−−−√2

x=−52+39−−√2icomplex solution

and

x=−52−39−−√2icomplex solution

Answer 2

Answer:

The answer is x^4+10x^3+35x^2+50x=96