SOLUTION: The sum of two numbers is 5. when the sum of the squares of the numbers is multiplied by 4 the result is 82. find the numbers. As a required first step, write down a system of two
Algebra.Com
Question 322493: The sum of two numbers is 5. when the sum of the squares of the numbers is multiplied by 4 the result is 82. find the numbers. As a required first step, write down a system of two equations in two unknowns whose solution solves the problem.
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
X+Y=5 OR X=5-Y
4(X^2+Y^2)=82
4[(5-Y)^2+Y^2]=82
4[25-10Y+Y^2+Y^2)=82
100-40Y+8Y^2=82
8Y^2-40Y+100-82=0
8Y^2-40Y+18=0
(2X-9)(4X-2)=0
2X-9=0
2X=9
X=9/2
X=4.5 ANS.
4X-2=0
4X=2
X=2/4
X=.5 ANS.
RELATED QUESTIONS
Find two numbers such that their sum multiplied by the sum of their squares is 65, and... (answered by mananth)
find two numbers such that their sum multiplied by the sum of their squares is 5500, and... (answered by oscargut)
find two numbers such that their sum multiplied by the sum of their squares is 5500, and... (answered by oscargut)
The sum of the squares of two numbers is 218 and their difference multiplied by the... (answered by math_tutor2020,Edwin McCravy,ikleyn,mccravyedwin)
When the sum of two woke numbers is multiplied by the difference of the numbers, the... (answered by ankor@dixie-net.com,MathTherapy)
when the sum of two whole numbers is multiplied by the difference of the number, the... (answered by Theo)
two numbers differ by 7 and the sum of their squares is 29. find the numbers (answered by JBarnum,Stitch)
two numbers differ by 2. The sum. of their squares is 244.find the numbers (answered by addingup,MathTherapy)
The sum of two numbers is 82.If twice the smaller number is subtracted from the larger... (answered by satyareddy22)