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
stiv31 [10]
2 years ago
13

The sum of three numbers in g.p. is 21 and the sum of their squares is 189. find the numbers.

Mathematics
1 answer:
sashaice [31]2 years ago
3 0
Let the three gp be a, ar and ar^2
a + ar + ar^2 = 21 => a(1 + r + r^2) = 21 . . . (1)
a^2 + a^2r^2 + a^2r^4 = 189 => a^2(1 + r^2 + r^4) = 189 . . . (2)
squaring (1) gives
a^2(1 + r + r^2)^2 = 441 . . . (3)
(3) ÷ (2) => (1 + r + r^2)^2 / (1 + r^2 + r^4) = 441/189 = 7/3
3(1 + r + r^2)^2 = 7(1 + r^2 + r^4)
3(r^4 + 2r^3 + 3r^2 + 2r + 1) = 7(1 + r^2 + r^4)
3r^4 + 6r^3 + 9r^2 + 6r + 3 = 7 + 7r^2 + 7r^4
4r^4 - 6r^3 - 2r^2 - 6r + 4 = 0
r = 1/2 or r = 2
From (1), a = 21/(1 + r + r^2)
When r = 2:
a = 21/(1 + 2 + 4) = 21/7 = 3
Therefore, the numbers are 3, 6 and 12.
You might be interested in
Stock prices fell 250 points one day and 60 points the next day. What is the average change in stock prices over the two days
arsen [322]

Answer:

the average change in stock prices over the two days is -155

Step-by-step explanation:

The computation of the average change in stock price over the two days is shown below:

= (-One day points - second day points) ÷ number of days

= (-250 points - 60 points ) ÷ 2 days

= -310 points ÷ 2 days

= -155

Hence, the average change in stock prices over the two days is -155

We simply applied the above formula so that the average change could come

3 0
2 years ago
Two angles of a triangle are the same size. The third angle is 3 times as large
Gnoma [55]
Use x to represent the first two angles. If the third angle is 3 times as large as the first, it can be represented as 3x. So, your angles are x, x, and 3x. These need to all add to 180 degrees, since it’s a triangle.

x + x + 3x = 180 —> Simplify the left side.
5x = 180 —> Divide by 5.
x = 36

So the first two angles are 36 degrees, and the third angle is 3 times that, which is 108 degrees.
3 0
3 years ago
Six values on the number line above are marked with letters. Which letters represent integers when the value on the number line
r-ruslan [8.4K]

Answer:

  A) L, N, O, P

Step-by-step explanation:

The even numbers on the number line are marked by the letters L, N, O, P.

_____

If a number gives an integer result when divided by 2, it is an even number. Zero is an even number, giving the integer zero when divided by 2.

6 0
3 years ago
Combine the like terms to create an equivalent expression:<br>-5r+8r+5​
Olegator [25]
Answer : 3r+5 hope this helps!
3 0
3 years ago
Is 0.06 bigger than 1?
taurus [48]

Hi there!


Great question! 0.06 is actually SMALLER than 1.


Why?


Because 0.06 is almost half of the whole number. Half of 1 is 0.5, which is larger than 0.06.

 

Half is smaller than whole, so, therefore, 1 is larger.


Hope this helps!

Message me if you need anything else! I'd be happy to help! :D

8 0
3 years ago
Read 2 more answers
Other questions:
  • Each pants leg on page 8 has an opening with a circumference of 8.5 inches. It took 15 stitches to make 3 inches in width. How m
    10·1 answer
  • A stadium brings in 16.25 million per year. It pays football related expenses of 13.5 million and stadium expenses of 2.7 millio
    5·1 answer
  • Companies with strong safety cultures usually have lower _____.
    13·2 answers
  • At the beginning of the recent period, there were 900 units of product in a department, 35% completed. these units were finished
    14·1 answer
  • Suppose that Ireland has placed a tariff of 12% on its exports and a tariff of 21% on its imports. If Ireland has tariff revenue
    11·1 answer
  • Which of the following metals needs roman numerals?
    8·2 answers
  • Express 60 km/h in metres per second.
    6·1 answer
  • Simplify the expression 5x + 4 + 9x =
    7·2 answers
  • Which expression is equivalent to 3x + 3 x + 3x <br><br> 3x3<br><br> 9x<br><br> 9x3<br><br> 27x
    14·1 answer
  • Multiply 6 times two-ninths.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!