1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Kryger [21]
3 years ago
6

A and B are postive integers such that 1/a + 1/b +1/ab = 1. Find ab

Mathematics
1 answer:
Kitty [74]3 years ago
4 0

Answer: ab =6

have:

\frac{1}{a}+\frac{1}{b}+\frac{1}{ab}=1\\\\=>\frac{b}{ab}+\frac{a}{ab}+\frac{1}{ab}=1\\\\\frac{a+b+1}{ab}=1

=> a + b + 1 = ab

⇔ a + b + 1 - ab = 0

⇔ b - 1 - a(b - 1) + 2 = 0

⇔ (b - 1)(1 - a) = -2

because a and b are postive integers => (b - 1) and (1 - a) also are integers

=> (b - 1) ∈ {-1; 1; 2; -2;}

(1 -a) ∈  {-1; 1; 2; -2;}

because (b -1).(1-a) = -2 => we have the table:

b - 1        -1             1              2             -2

1 - a         2            -2            -1              1

a              -1            3             2              0

b              0            2             3              -1

a.b            0           6             6               0

because a and b  are postive integers

=> (a;b) = (3;2) or (a;b) = (2;3)

=> ab = 6

Step-by-step explanation:

You might be interested in
3.25 + 3 tenths A.6.25 B.3.55
strojnjashka [21]

Answer:

b

Step-by-step explanation:

3.25+.3=3.55

4 0
3 years ago
Read 2 more answers
Did I do this right? What can I fix?
elena55 [62]
It looks right to me!!
6 0
3 years ago
What is the slope of the line?
yulyashka [42]

answer:

slope = \frac{y_2 - y_1}{x_2 - x_1}

that's how you find the slope in any equation

8 0
3 years ago
An angle measures 88° more than the measure of a complementary angle. what is the measure of each angle?
aleksandrvk [35]
Let one angle be x
Let second angle be 88+x
Sum of two complementary angles = 90°
x+ 88+ x = 90°
2x + 88 = 90
2x  = 90 - 88 = 2
x = 2/2 = 1

First angle = x = 1°
Second angle = 88 + x = 88+1 = 89°
I hope it is helpful:D
3 0
3 years ago
how many pounds of nuts selling for $9 per lb and raisins selling for $3 per lb should a person combine to obtain 60 lb of a tra
marta [7]
Let n be the number of lbs of nuts.
Let r be the number of lbs of raisins.
9n + 3r = 60 * 5 = 300 .............(1)
n + r = 60
n = 60 - r ...............(2)
Plugging the expression for n in (2) into (1) we get:
9(60 - r) + 3r = 300
which expands to:
540 - 9r + 3r = 300 .............(3)
Simplifying and rearranging (3) we get:
-6r = -240
Therefore r, the weight of raisins = 40 lbs
and the weight of nuts is 60 - 40 = 20 lbs
8 0
3 years ago
Other questions:
  • A photograph has a length that is 4 inches longer than its width, x. Its area is given by the expression x(x + 4). If the area o
    14·1 answer
  • 6.<br> HELP W THIS ONE TOO PLS!!
    14·1 answer
  • If​ Tucson's average rainfall is 12 and one fourth inches and​ Yuma's is 4 and four fifths ​inches, how much more​ rain, on the​
    13·1 answer
  • Calcular el área total del cubo si s=5√2
    15·1 answer
  • Find the distance between the two points rounding to the nearest tenth (if necessary).
    8·1 answer
  • (20PTS, Will mark brainliest!) What is the 8th term of the arithmetic sequence with a first term of 7 and a common difference of
    13·1 answer
  • James and Dan are partners in a small company. From each year’s profit, James is paid a bonus of $15000 and the remainder is sha
    6·1 answer
  • I need help with numbers 17 and 11. worksheet down below :) thank you. I'm using all my points so let this be the time I use my
    13·2 answers
  • Suppose City A is 50.2 km east of City B. City C is 124.4 km east of City B. How far apart are City A and City​ C?
    14·1 answer
  • What is the domain of the function represented by the graph?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!