i) Taking this as: x² - 16x + 14 = 0 and solving,

the two roots are: {8+5√2, 8-5√2}

Let u = 8+5√2 and v = 8-5√2

ii) So factorizing the given inequality is (x - u)*(x - v) < 0

For the product of two factors to be < 0, the factors must be opposite sign.

So x > u and x < v (or) x < u and x > v

In the first case, x > 8+5√2 and x < 8-5√2; as there is no intersection between these two limits, this is discarded.

In the second case, x < 8+5√2 and x > 8-5√2; this is possible.

So x in (8-5√2, 8+5√2);x is in (0.93, 15.07)

Number line you may mark yourself;

from 0.93 to 15.07, both limits excluded.