Mathematics, 27.07.2019 11:00 melaniegilbreath

If x/y+y/x=1 (x, y≠0) , find the value of x3 + y3.

If x/y+y/x=1 (x,y≠0) , find the value of x3 + y3.

Answers: 1

Show answers

Answers

Answer from: quissowavyquis7629

Answer: the value of x³ + y³ is 0.====== $\dfrac{x}{y} + \dfrac{y}{x} = 1$ combine the two fractions on the left-hand side of the equation. get a common denominator. the lcd between y and x is xy.multiply numerator and denominator of x/y by x: $\begin{aligned} \dfrac{x \cdot x}{y \cdot x} + \dfrac{y}{x} & = 1 \\ \dfrac{x^2}{xy} + \dfrac{y}{x} & = 1 \end{aligned}$ multiply numerator and denominator of y/x by y: $\begin{aligned} \dfrac{x^2}{xy} + \dfrac{y \cdot y}{x \cdot y} & = 1\\ \dfrac{x^2}{xy} + \dfrac{y^2}{xy} & = 1 \\ \dfrac{x^2 + y^2}{xy} & = 1 \end{aligned}$ multiply both sides of equation by xy: $\begin{aligned} xy \cdot \dfrac{x^2 + y^2}{xy} & = 1 \cdot xy \\ x^2 + y^2 & = xy \end{aligned}$ subtract both sides by xy: $\begin{aligned} x^2 + y^2 - xy & = 0 \\ x^2 - xy + y^2 & = 0 \\ \end{aligned}$ now x² - xy + y² is a part of a factoring identity. (the question asking for the value of x³ + y³ also hints at the use of this identity.)this factoring identity is the sum of cubes identity, which is as follows: $x^3 + y^3 = (x+y)(x^2 - xy + y^2)$ notice how we have x² - xy + y² in that factoring identity. if you multiply x² - xy + y² by x+y, you get x³ + y³.therefore, with our equation, multiply both sides by (x+y): $(x+y)(x^2 - xy + y^2)= 0 \cdot (x+y)$ the right-hand side stays 0.the left-hand side can change, according to the identity, into x³ + y³ becausex³ + y³ = (x+y)(x² - xy + y²) $x^3 + y^3 = 0$ the value of x³ + y³ is 0.
If x/y+y/x=1 (x,y≠0) , find the value of x3 + y3.

If x/y+y/x=1 (x,y≠0) , find the value of x3 + y3.

Answer from: Quest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer: (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

Answer from: Quest

50*10 is greater

step-by-step explanation:

if you add the zero from 10 to 50, it will give you a bigger number.

Another question on Mathematics

Mathematics, 21.06.2019 16:30

Asequence {an} is defined recursively, with a1 = 1, a2 = 2 and, for n > 2, an = an-1 an-2 . find the term a241

Answers: 2

Answer

Mathematics, 21.06.2019 22:50

Which best explains why this triangle is or is not a right triangle ?

Answers: 2

Answer

Mathematics, 22.06.2019 00:10

How do i take any fraction and make it into a decimal or percentage?

Answers: 1

Answer

Mathematics, 22.06.2019 00:50

To diagonalize an nxn matrix a means to find an invertible matrix p and a diagonal matrix d such that a pdp d p ap or [1 3 dh epap 3 let a=-3 -5 -3 3 3 1 step 1: find the eigenvalues of matrix a "2's" step 2: find the corresponding eigenvectors of a step 3: createp from eigenvectors in step 2 step 4 create d with matching eigenvalues.

Answers: 3

Answer

You know the right answer?

If x/y+y/x=1 (x, y≠0) , find the value of x3 + y3.
...

Questions