MathMaster logo

MathMaster

  1. Home
  2. general
  3. if x y 3 and xy 2 then x 3 x 1 y 3 y 1
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
106 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 area of a regular hexagon with a side length of 7 units?
+
Which interval(s) does the tangent function have a positive value?
+
Math Question: What is the area of a triangle with side lengths 5, 7, and 9 using Heron’s Formula?
+
New questions in Mathematics
-442/c+5=26 what is c?
-6n+5=-13
A college believes that 22% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 5 percentage points?
12-6x=4x+2
Convert 78 percent to a decimal
Find the equation of the line perpendicular to −5𝑥−3𝑦+5=0 passing through the point (0,−2)
How many anagrams of the word STROMEC there that do not contain STROM, MOST, MOC or CEST as a subword? By subword is meant anything that is created by omitting some letters - for example, the word EMROSCT contains both MOC and MOST as subwords.
How many anagrams of the word SROMEC there that do not contain STROM, MOST, MOC or CEST as a subword? By subword is meant anything that is created by omitting some letters - for example, the word EMROSCT contains both MOC and MOST as subwords.
suppose random variable x follows poisson distribution with expected value 3. what is variance of x?
It is known that the content of milk that is actually in a bag distributes normally with an average of 900 grams and variance 25 square grams. Suppose that the cost in pesos of a bag of milk is given by 𝐶(𝑥) = { 3800 𝑠𝑖 𝑥 ≤ 890 4500 𝑠𝑖 𝑥 > 890 Find the expected cost.
89, ÷ 10
If X1 and X2 are independent standard normal variables, find P(X1^2 + X2^2 > 2.41)
Convert 9/13 to a percent
Give an example of a function defined in R that is continuous in all points, except in the set Z of integers.
How to convert 45 kg into grams
Two particles of electrical charges Q1=3.8×10-⁶C and q,=4.4×10-⁶C are separated in vacuum by a distance of 4.0.10-⁸ m. Since K=9.0.10⁹ N.m²/C², the intensity of the interaction force between them, in newtons, is?
Solve the following 9x - 9 - 6x = 5 + 8x - 9
How much does 7.2 moles of ammonium dichromate weigh? (NH4)2Cr2O7
A group of 17 people spent 9 days on vacation and spent R$776.34 on barbecue meat and the bill needs to be divided as follows: 6 people stayed for 9 days, 7 people stayed for 4 days, and 2 people stayed for 5 days and 2 people stayed 3 days, how much does each group have to pay for the days they stayed?
Dano forgot his computer password. The password was four characters long. Dano remembered only three characters: 3, g, N. The last character was one of the numbers 3, 5, 7, 9. How many possible expansions are there for Dano's password?

You might be interested in