What is (x-1)(x-5)>4 ?

The solution to (x-1)(x-5)>4 is x 2sqrt(2)+3

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(x-1)(x-5)>4

(x - 1) (x - 5) > 4

x < - 22 + 3 or x > 22 + 3

Interval Notation

(- \infty, - 22 + 3) \cup (22 + 3, \infty)

Decimal Notation

x < 0.17157 \dots or x > 5.82842 \dots

Solution steps

(x - 1) (x - 5) > 4

Rewrite in standard form

x^{2} - 6 x + 1 > 0

Complete the square

x^{2} - 6 x + 1 : (x - 3)^{2} - 8

(x - 3)^{2} - 8 > 0

Move

8

to the right side

(x - 3)^{2} > 8

For

u^{n} > a

, if

n

is even then

x - 3 < - 8 or x - 3 > 8

x - 3 < - 8 : x < - 22 + 3

x - 3 > 8 : x > 22 + 3

Combine the intervals

x < - 22 + 3 or x > 22 + 3

\frac{x - 4}{x + 2} < 0

\frac{( 3 x + 4 )}{( 5 x + 3 )} < \frac{( x + 2 )}{( 2 x + 3 )}

x^{2} + 3 < 7

\frac{( x ^{2} - 1 )}{( x ^{2} + x + 1 )} < 0

2 t^{2} - 7 t + 6 < 0

What is (x-1)(x-5)>4 ?
The solution to (x-1)(x-5)>4 is x<-2sqrt(2)+3\lor x>2sqrt(2)+3