Question

Solve: (x – 4)(x – 2)(x- 7)(x + 1) = 16

Answer 1

(x – 4)(x – 7) (x – 2)(x + 1) = 16

⇒ (x – 4)(x – 2)(x – 7)(x + 1) = 16

⇒ (x² – 6x + 8)(x² – 6x – 7) = 16

Let x² – 6x = y

(y + 8)(y – 7) = 16

⇒ y² – 7y + 8y – 56 – 16 = 0

⇒ y² + y – 72 = 0

⇒ (y + 9)(y – 8) = 0

y + 9 = 0

x² – 6x + 9 = 0

(x – 3)² = 0

x = 3, 3

or

y – 8 = 0

x² – 6x – 8 = 0

x = `(6 +- sqrt(36 - 4(1)(- 8)))/(2(1))`

= `(6 +- sqrt(36 + 32))/2`

= `(6 + sqrt(68))/2`

= `(6 +- 2sqrt(17))/2`

= `2 ((3 +-  sqrt(17)))/2`

= `3 + sqrt(17)`

Roots are `3, 3, 3 +- sqrt(17)`