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
mixas84 [53]
3 years ago
7

Let a and b be real numbers satisfying a^3 - 3ab^2 = 47 and b^3 - 3a^2 b = 52. Find a^2 + b^2.

Mathematics
1 answer:
boyakko [2]3 years ago
8 0

Answer: a²+b² = -99/2

Step-by-step explanation:

Since we are given two equations, this equations will be solved simultaneously to get a² and b²

a³ - 3ab² = 47 ... 1

b³ - 3a² b = 52... 2

From 1, a(a² - 3b²) = 47...3

From 2, b(b² - 3a²) = 52... 4

Adding 3 and 4, we have;

a²+b²-3b²-3a² = 99 (note that a and b will no longer be part of the equations as they have been factored out)

a²+b²-(3b²+3a²) = 99

(a²+b²) -3(b²+a²)= 99

Taking the difference we have

- 2(a²+b²) = 99

a²+b² = -99/2

You might be interested in
The sum of two numbers is 21,and their difference is 9
Ghella [55]
let's say the two numbers are x and x + 9. so we know x + x + 9 = 21, so 2x + 9 = 21. subtract 9 from both dies to get 12 = 2x. divide both sides by 2 to get x = 6. so your two numbers are 6 and 15.
3 0
3 years ago
Read 2 more answers
For each system of equations, drag the true statement about its solution set to the box under the system.
neonofarm [45]

Answer:

Step-by-step explanation:

3 0
3 years ago
Please help solve this. (Answer is not 80)
blondinia [14]

Answer:

70

Step-by-step explanation:

180 -(60+65) = 180 - 125 = 55

180 - (50 + 55) = 180 - 105 = 75

180 - (35 + 75) = 180 - 110 = 70

3 0
3 years ago
Read 2 more answers
PLEASE HELP I WILL MARK BRAINLIEST!!!!
guapka [62]

Answer:

Math-way

Step-by-step explanation:

I'd do it for you right now if you wanted but it'd be much faster if you did it, It's is perfect for this problem

8 0
3 years ago
Please help me solve step by step it's urgent​
NNADVOKAT [17]

Answer:

2i: 169.71

2ii: 0.17L

3a: 4×10⁻⁵

3b: 110011

Step-by-step explanation:

2i. The surface of the top and bottom of the tin is two times (top and bottom) π·r² = 2·π·3² = 18π cm².

The circumference of the circle is 2·π·r = 6π cm².

The area of the material connecting top and bottom is a rectangle of the tin height times the circumference: 6·6π = 36π cm².

This gives a total of  18π + 36π = 54π  cm².

With π approximated by 22/7 the total surface area is 54*22/7 ≈ 169.71.

Notice how the calculation is simple by waiting until the very last moment to substitute π.

2ii. The volume is the area π·r² of the circle times the height of the tin: 9π*6 = 54π cm³ ≈ 169.71 cm³.

Since 1L = 1000 cm³ the volume is 0.16971 litres, which should be rounded to 0.17 L.

3a: If we rewrite P as 36 x 10⁻⁴ and realize that 36/2.25 = 16, then the fraction can be written as

16 x 10⁻⁴⁻⁶ = 16 x 10⁻¹⁰.

The square root of that is taking it to the power of 1/2, so (16x10⁻¹⁰)^0.5 = 4x10⁻⁵ = 0.00004

3b: 1111 1111 is 255 in decimal. 101 is 5 in decimal. 255/5 is 51 in decimal. 51 in binary is 110011.

6 0
4 years ago
Other questions:
  • What are the next three terms of each sequence?<br><br><br><br> -2, 4
    5·1 answer
  • PLS HELP ME...THX
    11·1 answer
  • How do I know what is the segment of a triangle?​
    15·1 answer
  • What is the written form of the decimal number .954?
    14·2 answers
  • What is 0.92 is 10 times as much as................
    10·1 answer
  • What is 8 1/6 + 3/4​
    14·2 answers
  • Simplify i^12. a. 1 b. −1 c. −i d. i
    12·1 answer
  • I need help w number 6
    8·2 answers
  • Which equation has x = 5 as the solution
    12·2 answers
  • If a mechanic takes 4 hours to complete 8 car inspections, at what rate are the cars being inspected?
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!