SOLUTION: Find two numbers such that their sum is 10 and their product is 22.

Question 101116This question is from textbook Algebra for College Students
: Find two numbers such that their sum is 10 and their product is 22. This question is from textbook Algebra for College Students

Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
A)x+y=10
B)xy=22
.
y=22/x from B)
.
x+(22/x)=10 substitute 22/x for y in A)
x^2+22=10x multiply x times each side.
x^2-10+22=0
Quadratic formula: x=5+sqrt(3) or x=5-sqrt(3)
.
When x=5+sqrt(3) y=10-(5+sqrt(3))=10-5-sqrt(3)=5-sqrt(3)
When x=5-sqrt(3) y=10-(5-sqrt(3))=10-5+sqrt(3)=5+sqrt(3)
.
Check:
5+sqrt(3)+5-sqrt(3)=10
(5+sqrt(3))*(5-sqrt(3))=25-3=22
Ed

RELATED QUESTIONS
Find two numbers such that their sum is 10 and their product is 22? (answered by richard1234)

To be perfectly honest to you...I suck at word problems. Here is the problem; Find two (answered by checkley71)

FIND TWO NUMBERS SUCH THAT THEIR SUM IS 6 AND THEIR PRODUCT IS... (answered by prabhjyot)

find two positive numbers such that their sum is 25 and their product is a... (answered by chriswen)

Find two numbers such that their sum is 302 and their product is... (answered by ewatrrr)

Find two numbers such that their sum is 6 and their product is... (answered by rothauserc)

Find two numbers such that thier sum is 8 and their product is... (answered by ewatrrr)

find two consecutive odd natural numbers such that their product is 223 more than their... (answered by Alan3354)

the sum of two numbers is 22 and their product is 120. Find the two... (answered by Fombitz,MathLover1)