Theo mình thì thế này :
\(x\left(x+4\right)\left(x+5\right)\left(x+9\right)+91\)
= \(\left[x.\left(x+9\right)\right]\left[\left(x+4\right)\left(x+5\right)\right]+91\)
= \(\left(x^2+9x\right).\left(x^2+9x\right)+91\)
Đặt \(t=\left(x^2+9x\right)\)
=> \(t^2+91\)
=> \(\left(x^2+9x\right)^2+91\)
=> \(x^4+19x^2+81x^2+91\)
x(x+4)(x+5)(x+9)= 91
=> x. x( 4+5+9) =91
=> x.x . 18= 91
=> x.x= 73
=> \(x^2=\) 73
=> x=\(\sqrt{73}\)
\(x\left(x+4\right)\left(x+5\right)\left(x+9\right)+91\)
\(=\left(x^2+4x\right)\left(x+5\right)\left(x+9\right)+91\)
\(=\left(x^3+5x^2+4x^2+20x\right)\left(x+9\right)+91\)
\(=x^4+5x^3+4x^3+20x^2+91\)
\(=x^4+9x^3+20x^2+91\)
\(x\left(x+4\right)\left(x+5\right)\left(x+9\right)+91\\ =x\left(x+9\right)\left(x+4\right)\left(x+5\right)+91\\ =\left(x^2+9x\right)\left(x^2+9x+20\right)+91\)
Đặt x^2+9x=t
Ta có :
\(t\left(t+20\right)+91\\ =t^2+20t+91\\ =\left(t^2+2.t.10+100\right)-9\\ =\left(t-10\right)^2-9\\ =\left(t-13\right)\left(t-7\right)\\ =\left(x^2+9x-13\right)\left(x^2+9x-7\right)\)
