Sum/difference:
Let
This means that
Now, assume that is rational. The sum/difference of two rational numbers is still rational (so 5-x is rational), and the division by 3 doesn't change this. So, you have that the square root of 8 equals a rational number, which is false. The mistake must have been supposing that was rational, which proves that the sum/difference of the two given terms was irrational
Multiplication/division:
The logic is actually the same: if we multiply the two terms we get
if again we assume x to be rational, we have
But if x is rational, so is -x/15, and again we come to a contradiction: we have the square root of 8 on one side, which is irrational, and -x/15 on the other, which is rational. So, again, x must have been irrational. You can prove the same claim for the division in a totally similar fashion.
a + b = 60 (1)
b < a with 6 ⇒ b = a - 6 (2)
(1), (2) ⇒ a + a - 6 = 60 ⇒ a + a = 60 + 6 ⇒ 2a = 66 ⇒ a + 66:2 ⇒
⇒ a = 33 (3)
(2), (3) ⇒ b = 33 - 6 ⇒ b = 27
So, the numbers are : a = 33, b = 27
Answer:
151°
Step-by-step explanation:
126°+221°+95°+57°+70+x=720° ( sum of interior angles of hexagon)
x + 569° =720°
x = 720°- 569°
=151°
Answer:
kkk
Step-by-step explanation: