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]
3 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]3 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
Which equation is equivalent to 24x = 8x-3?
Elena-2011 [213]

Answer:

uh maybe 16x= -3 or x= -3/16

Step-by-step explanation:

I'm so sorry if this is wrong or not what you're looking for

3 0
3 years ago
Read 2 more answers
Can someone help me with these questions? i’m so lost
spayn [35]

Answer:

Q.5 ab=cd

Q.6 ad=bc

Q.7 ce=ae

Q.8 eb=ed

Q.9 angle D=angle B (opposite angle of parallelogram are equal)

let other angle of parallelogram be x.

angle A+angle B +angle C + angle D= 360° (sum of quadrilateral is 360°)

x+130°+x+130°=360°

2x+260°=360°

2x=360°-260°

2x=100°

x=100/2

x=50°

Q.10 similarly, angle b= angle d

let other angle be x.

x+61°+ x+61°=360°

2x+122°=360°

2x=360°+122°

2x=238°

x=238°/2

x=119°

Q.11 in quadrilateral opposite angles are equal and opposite angle of parallelogram are equal.

Q.12 in quadrilateral opposite angle are equal and opposite angle of parallelogram are equal.

Q.13 in quadrilateral opposite sides are equal and opposite sides are parellel and this property is also present in parallelogram.

q.14 in quadrilateral diagonal bisected each other and diagonal of parallelogram also bisect each other.

8 0
3 years ago
Find the minimum value if f(x) = xe^x over [-2,0]
SashulF [63]

Given function:

f(x)=xe^x

The minimum value of the function can be found by setting the first derivative of the function to zero.

f^{\prime}(x)=xe^x+e^x\begin{gathered} xe^x+e^x\text{ = 0} \\ e^x(x\text{ + 1)  = 0} \end{gathered}

Solving for x:

\begin{gathered} x\text{ + 1 = 0} \\ x\text{ = -1} \end{gathered}\begin{gathered} e^x\text{ = 0} \\ \text{Does not exist} \end{gathered}

Substituting the value of x into the original function:

\begin{gathered} f(x=1)=-1\times e^{^{-1}}_{} \\ =\text{ -}0.368 \end{gathered}

Hence, the minimum value in the given range is (-1, -0.368)

6 0
1 year ago
I need help with both pictures plz
jeyben [28]

Answer:

-25+12 is less

Step-by-step explanation

1st picture

-25+12=-13

40+-63=-23

2nd picture

Negative

Positive

Negative Negative

To find the answers just simply do the number in a calculator for example -6+64 put that in a calculator and it will help you. figure our number 5

5 0
3 years ago
Simplify the expression.<br><br> 55−4⋅5+12
Lunna [17]
Your answer is 62.5. Hope i helped
4 0
3 years ago
Read 2 more answers
Other questions:
  • Ann needs 42feet of fabric to make a small quilt how many yards of fabric should she buy?
    10·2 answers
  • Find the mileage for a car that travels 576 miles on 18 gallons of gas.
    13·2 answers
  • 5g + 4(-5+3g) = 1 - g
    8·2 answers
  • What is the distance between (14,4) and (15,8)
    10·1 answer
  • An 11 letter word for the variable in an algebraic expression
    8·2 answers
  • Samuel is going to invest $4,900 and leave it in an account for 14 years. Assuming the
    12·1 answer
  • Suppose there are approximately 220 calories in 3 servings of a particular brand of cereal and 362 calories in 5 servings of the
    7·1 answer
  • Lois makes customised tee-shirts. She advertises and receives orders through her own website. She buys blank tee-shirts for $1 e
    5·1 answer
  • Salma received 7/9 of the 81 votes cast for class president. How many votes did she receive?
    8·2 answers
  • Drag the tiles to the correct boxes to complete the pairs.
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!