$MathMaster logo$

MathMaster

Home
general
two numbers differ by 7 and the sum of their squares is 29 find the numbers

Question

Two numbers differ by 7, and the sum of their squares is 29. Find the numbers.

280

likes

1400 views

Answer to a math question Two numbers differ by 7, and the sum of their squares is 29. Find the numbers.

$Expert avatar$

4.7

109 Answers

let numbers are x and y. then x-y=7...............(1) and x^2+y^2=29 From (1), \left(x-y\right)^2=49 x^2+y^2-2xy=49 29-2xy=49 xy=-10 then y=-10/x, Now from (1), x+\frac{10}{x}=7 x^2-7x+10=0 so x=2,5, then y=-5,-2 So the numbers are 2,-5 or 5,-2

Frequently asked questions (FAQs)

What is the vertex of the parabola represented by the equation 𝑦 = 3𝑥^2 + 2𝑥 + 1?

+

What is the solution to the inequality 3x + 5 < 20?

+

What is the sum of cubes for any three positive integers, each raised to the power of 3?

+

New questions in Mathematics

A particular employee arrives at work sometime between 8:00 a.m. and 8:40 a.m. Based on past experience the company has determined that the employee is equally likely to arrive at any time between 8:00 a.m. and 8:40 a.m. Find the probability that the employee will arrive between 8:05 a.m. and 8:30 a.m. Round your answer to four decimal places, if necessary.

a to the power of 2 minus 16 over a plus 4, what is the result?

reduction method 2x-y=13 x+y=-1

a ferry travels 1/6 of the distance between two ports in 3/7 hour. the ferry travels at a constant rate. at this rate, what fraction of the distance between the two ports can the ferry travel in one hour?

5 squirrels were found to have an average weight of 9.3 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight

A car that starts from rest moves for 11 min, reaching a speed of 135 km/h, calculate the acceleration it had

A consulting company charges a fee of $50 per hour for consulting. If their monthly fixed costs are $1,000 and they want to make a monthly profit of $2,500, how many consulting hours should they bill per month?

Solve the math problem 400 students are asked if they live in an apartment and have a pet: Apartment: 120 Both: 30 Pet: 90 The probability that a randomly selected student not living in an apartment has a pet is

If eight basketball teams participate in a tournament, find the number of different ways that first, second, and third places can be decided assuming that no ties are allowed.

Two events E and F are ________ if the occurrence of event E in a probability experiment does not affect the probability of event F.

A job takes 9 workers 92 hours to finish. How many hours would it take 5 workers to complete the same job?

To celebrate the five-year anniversary of a consultancy specializing in information technology, the administrator decided to draw 3 different qualification courses among its 10 employees. Considering that the same employee cannot be drawn more than once, the total number of different ways of drawing among employees is:

A pair of die is thrown and the absolute difference of the two scores is recorded. What is the probability of the absolute difference being 4 or more?

(1) July 1, 2008: Receives $25,000 from Quinn Zealick for 25,000 shares of the stock common face value $1 from the bookstore. (2) July 1, 2008: Obtains $30,000 loan from local bank for needs of working capital. The loan earns 6% interest per year. The loan is payable with interest on June 30, 2009. (3) July 1, 2008: Sign a three-year rental agreement at an annual rent of $20,000 Pay the first year's rent in advance. (4) July 1, 2008: Purchases shelves for $4,000 in cash. The shelves have an estimated useful life of five years and zero residual value. (5) July 1, 2008: Purchase computers for $10,000 in cash. The computers They have an estimated useful life of three years and $1,000 in residual value. (6) July 1, 2008: Makes guarantee deposits with various book distributors for a total of $8,000. Deposits are refundable on June 30, 2009 if the bookstore pays on time all amounts payable for books purchased from distributors between July 2008 and June 30, 2009. (7) During 2008: Purchases books on account from various distributors for a cost of $160,000. (8)During 2008: Sells books costing $140,000 to $172,800. Of the total sales, $24,600 corresponds to cash and $148,200 is on account. (9) During 2008: Returns unsold books and books ordered in error for a cost of $14,600. The company had not yet paid for these books. (10) During 2008: Collected $142,400 from sales on account. (11) During 2008: Pays employees salaries of $16,700. (12) During 2008: Pays $139,800 to book distributors of the amounts payable for purchases on account. (13) December 28, 2008: Receives customer advances of $850 due to order books special that the bookstore will order and expects to receive during 2009. (14) December 31, 2008: Record the corresponding amount of interest expense on the loan in (2) for 2008. (15) December 31, 2008: Record the corresponding amount of rental expense for 2008. (16) December 31, 2008: Record the corresponding amount of depreciation expense on the shelves in (4). (17) December 31, 2008: Record the corresponding amount of depreciation expense about computers in (5). (18) December 31, 2008: Record the corresponding amount of income tax expense. profits for 2008. The income tax rate is 40%. The taxes are paid on March 15, 2009. (1) March 15, 2009: Pays 2008 income tax. (2) June 30, 2009: Pay off the bank loan with interest. (3) July 1, 2009: Obtains a new bank loan for $75,000. He loan is payable on June 30, 2010, with 8% interest payable to the expiration. (4) July 1, 2009: Receives security deposits from book distributors. (5) July 1, 2009: Pay the rent corresponding to the period from July 1 2009 to June 30, 2010. (6) During 2009: Purchase books on account for a cost of $310,000. (7)During 2009: Sold books for a cost of $286,400 for $353,700. Of the total sales, $24,900 corresponds to cash, $850 corresponds to special orders received during December of 2008 and $327,950 are on account. (8) During 2009: Returns unsold books at a cost of $22,700. The company has not yet I had paid for these books. (9) During 2009: Collects $320,600 from sales to accounts. (10) During 2009: Pays employees compensation of $29,400. (11) During 2009: pays $281,100 to book distributors for book purchases from account. (12) December 31, 2009: Declares and pays a dividend of $4,000.

The market for economics textbooks is represented by the following supply and demand equations: P = 5 + 2Qs P = 20 - Qd Where P is the price in £s and Qs and Qd are the quantities supplied and demanded in thousands. What is the equilibrium price?

How to do 15 x 3304

Give an example of a function defined in R that is continuous in all points, except in the set Z of integers.

8/9 divided by 10/6

A membership to the gym cost $25 per person in 1995. The membership cost has increased by an average $6 per person for each year since 1995. Write a linear equation for the cost of a gym membership for one person since 1995. What is the cost of a gym membership in 2009?