Question

if x+y=3 and xy=-2 then (x^3+x+1)×(y^3+y+1)

63

likes
314 views

Answer to a math question if x+y=3 and xy=-2 then (x^3+x+1)×(y^3+y+1)

Expert avatar
Jayne
4.4
25 Answers
(x^3+x+1)×(y^3+y+1)=x^3y^3+x^3y+xy^3+x^3+xy+x+y^3+y+1 So that: =(xy)^3+ xy(x^2+y^2)+xy+(x+y)+(x^3+y^3)+1 Now put xy=-2, and x+y=3: =(-2)^3+ (-2)(x^2+y^2)+(-2)+3+(x^3+y^3)+1 =-8-2(x^2+y^2)-2+3+(x^3+y^3)+1 =-6-2(x^2+y^2)+(x^3+y^3) Now to calculate x^2+y^2 use: (x+y)^2=3^2 x^2+y^2+2xy=9 x^2+y^2+2(-2)=9 x^2+y^2-4=9 x^2+y^2=13 and: x^3+y^3=(x+y)(x^2+y^2-xy)=3(13-(-2))=3(13+2)=3(15)=45 So that: =-6-2(x^2+y^2)+(x^3+y^3)=-6-2(13)+45 =-6-26+45 =-32+45 (x^3+x+1)×(y^3+y+1)=13

Frequently asked questions (FAQs)
What is the result of multiplying a vector by a scalar quantity?
+
Math question: What is the limit as x approaches 5 of (2x^2 - 3x + 1)/(x - 5)?
+
What is the derivative of sin(2x)?
+
New questions in Mathematics
Write 32/25 as a percent
Kayla has $8,836.00 in her savings account. The bank gives Kayla 5%of the amount of money in account as a customer bonus. What amount of money does the bank give Kayla? Justify your answer on a 6th grade level.
A bird randomly chooses to land on 1 of 12 perches available in its aviary. Determine the Probability of it landing on a perch numbered 8 and then on a perch marked with a prime number; take into account that he never lands on the same perch in the sequence.
How many different ways can a psychology student select 5 subjects from a pool of 20 subjects and assign each one to a different experiment?
2.3/-71.32
If you randomly selected one person from the 900 subjects in this study, what is the probability that the person exhibits the minimum BMI?
A company that manufactures personal hygiene items purchases machinery for $220,000 that is considered to last 7 years; it is estimated that at the end of the period it will have a salvage value of $1000. Find: to. The depreciation rate. b. The book value at the end of the sixth year.
The ninth term of a given geometric progression, with reason q , is 1792, and its fourth term is 56. Thus, calculate the fourth term of another geometric progression, whose ratio is q +1 and whose first term is equal to the first term of the first P.G. described.
Exercise 1 An ejidal association wishes to determine the distribution for the three different crops that it can plant for the next season on its available 900 hectares. Information on the total available and how many resources are required for each hectare of cultivation is shown in the following tables: Total available resource Water 15,000 m3 Fertilizer 5,000 kg Labor 125 day laborers Requirements per cultivated hectare Corn Soybeans Wheat Water 15 25 20 Fertilizer 5 8 7 Labor** 1/8 1/5 1/4 *The data in fraction means that with one day laborer it will be possible to care for 8, 5 and 4 hectares respectively. * Sales of crops 1 and 3, according to information from the Department of Agriculture, are guaranteed and exceed the capacity of the cooperative. However, soybeans must be limited to a maximum of 150 hectares. On the other hand, the profits for each hectare of crop obtained are estimated at: $7,500 for corn, $8,500 for soybeans and $8,000 for wheat. The objectives are to determine: • How many hectares of each crop must be allocated so that the profit is maximum. R= • The estimated profits for the ejidal cooperative in the next growing season. R=
For what values of m is point P (m, 1 - 2m) in the 2⁰ quadrant?
Your grandfather has run a small high street pharmacy for 40 years. After much persuasion, he has agreed to open a digital store online. List 5 potential ways to improve sales and/or margins by having a digital pharmacy through the utilisation of historic or new sales data.
A company made 150,000 in the first year 145,000 in the second 140,000 in the third year successively during the first decade of this company's existence it made a total of
A building lot is in the shape of a triangle with a base of 133 feet and a height of 76 feet. What is it's area in square feet?
Let f and g be defined in R and suppose that there exists M > 0 such that |f(x) − f(p)| ≤ M|g(x) − g(p)|, for all x. Prove that if g is continuous in p, then f will also be continuous in p.
16.What payment (deposit) made at the end of each month will accumulate to $10473 in 13 years at 7.9% compounded monthly? Enter to the nearest cent (two decimals). Do not use $ signs or commas in the answer.
A psychologist is investigating the levels of test anxiety in various university courses. Anxiety is measured on a scale ranging from 0 to 100, where 0 indicates the complete absence of anxiety and 100 represents an extreme level of anxiety. From the data obtained, it has been discovered that the psychology score is triple that of nursing, and in turn, the latter has a score 10 points lower than the nutrition major. Furthermore, the score in the veterinary degree is 15 points higher than that of nutrition. Finally, if we add the scores of all the races, we will obtain a total of 173 points. Pose the equation that represents the situation described in the previous problem and determine: What is the score that psychology obtained regarding its anxiety level before the exams?
A nondegenerate ideal gas of diatomic molecules with a kilomolar mass of 2 kg/kmol and a characteristic rotational temperature of 86 K is adsorbed on the walls of a container, where the binding energy is 0.02 eV. The adsorbed molecules move freely on the walls, and their rotation is confined to the plane of the walls. Calculate the surface density of adsorbed molecules at 12 K if the gas pressure is 103 Pa! What result would you get at 68 K and the same pressure?
The slope of the tangent line to the curve f(x)=4tan x at the point (π/4,4)
Carmen's age was twice as old as Luis was when Carmen was Luis's age. When Luis is Carmen's age, their ages will add up to 112.
The car with an irresponsible driver starts to brake when it goes through a red light. When passing the traffic light, he does so at a speed of 115 kph in the right lane. Further ahead, 70 meters from the traffic light, a child is crossing the street and falls. If the effect of the car's brakes is equivalent to a deceleration of magnitude 5.7m/s². Is the child hit by the car or not? How far from the traffic light does the car stop?