Posted by Anonymous on Wednesday, April 13, 2011 at 12:54am.
Suppose x and y are real numbers such that xy = 9 and x2y + xy2 + x + y = 100. What is the integer value of x2 + y2? (Target Round #6)
- 8th grade math - Jai, Wednesday, April 13, 2011 at 1:19am
observe that we can factor xy from (x^2)y + x(y^2):
(x^2)y + x(y^2) + x + y = 100:
xy [ x + y ] + x + y = 100
then we can factor (x + y):
(x + y)(xy + 1) = 100
since xy = 9,
(x + y)(9 + 1) = 100
(x + y)(10) = 100
x + y = 10
getting its square,
(x + y)^2 = 100
x^2 + 2xy + y^2 = 100
since xy = 9,
x^2 + y^2 + 2*9 = 100
x^2 + y^2 + 18 = 100
x^2 + y^2 = 82
hope this helps~ :)
Answer This Question
More Related Questions
- Math- calculus - Suppose f is a function which satisfies the properties: f(x+y)=...
- Math - TRUE OR FALSE ? Justify your answer. a. There exist real numbers a and b ...
- calculus - calculate Äƒ/Äx and Äƒ/Äy. ƒ(x,y) = xy² + x²y
- Algebra - What is the smallest integer value of c such that the function f(x)=x...
- c++ - Write a program that asks the user to input a grade that he or she ...
- math - If p and q are real numbers such that p>5 and q>4, what is the ...
- 8th Grade Math - Please help! Which statement is false? A. The number zero is a ...
- Algebra 1 - Which statement about real numbers is true? Across the heading says...
- 7th grade math Ms.Sue please - 1. Which of these numbers can be classified as ...
- math - Translate the following English sentence into a symbolic sentence with ...