19)
solve the quadratic equation x2 − 18x + 81 = 64 for x.

a)
x = 17 or x = 1

b)
x = 11 or x = −5

c)
x = 9 or x = −8

d)
x = 2 or x = 9

{1, 17}

Step-by-step explanation:

x2 − 18x + 81 = 64 can be rewritten as x² - 18x + 81 = 64.

Next, x² - 18x + 81 can be rewritten as (x - 9)²

so that we now have:

(x - 9)² = 64.

Taking the sqrt of both sides, we get

x - 9 = ± 8

Then one root is x = 9 + 8 = 17, and the other is x = 9 - 8 = 1.

{1, 17} is the set of roots

4+  2 and 2+  2

Step-by-step explanation:

A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator and the denominator are whole numbers.  

On the other hand, all numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction.

So, let us take two irrational numbers a=4+  2  and b=2+ 2  and we now calculate a−b as follows:  a−b=(4+  2  )−(2+  2)=4+  2 −2−  2 =2=  1 2

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Therefore, the difference of two irrational numbers a and b is 2 and from the above defination of rational numbers, we get that 2 is a rational number.

Hence, the difference of two irrational numbers 4+  2 and 2+  2  is a rational number.