SOLUTION: The sum of the squares of two numbers is 90. The difference between them is 6. Find the numbers?

Question 332684: The sum of the squares of two numbers is 90. The difference between them is 6. Find the numbers?
Found 2 solutions by mananth, benazir.sj@gmail.com:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
x^2+y^2=90
x-y=6
(x-y)^2= 36
x^2+y^2-2xy=36
90-2xy= 36
2xy=90-36
2xy=54
xy=54/2
xy=27
divide by y
x=27/y.
..
plug the value of x in equation (x-y)=6
27/y - y =6
27-y^2 / y =6
27-y^2=6y
y^2+6y-27=0
x^2+9x-3x-27=0
x(x+9)-3(x+9)=0
(x+9)(x-3)=0
x=-9 OR 3
..
x=27/y
x=-9
-9=27/y
y=27/-9
y=-3
(-9,-3)
..
x=27/y
x= 3
y=27/3
y= 9
(3,9)
Answer by benazir.sj@gmail.com(109) (Show Source): You can put this solution on YOUR website!

sum of squares of two numbers is
a^2 + b^2 = 90
differnce between two numbers
a - b = 6
then
a = 6 + b
(6 + b)^2 + b^2 = 90
36 + 12b + 2b^2 = 90
2b^2 + 12b - 54 = 0
b^2 + 6b - 27 = 0 (factoring)
b^2+9b -3b -27 =0
b(b+9) -3(b+9)
(b+9)(b-3)
b=-9,3since we have to take the positive number b=3
a=6+3=9
therefore the two numbers are 3and 9
RELATED QUESTIONS
The difference of two positive numbers is 6 and the sum of their squares is 90. Find the... (answered by solver91311)
The sum of two numbers is 135. The difference between them is 9. Find the... (answered by nerdybill)
The difference between two numbers is 2, and the sum of their squares is 52. Find the... (answered by jorel555)
The sum of two numbers is 8 and the difference between their squares is 34. Find their... (answered by rakhileshnaidu,Alan3354)
the difference between the squares of two consecutive numbers is 31. find the... (answered by richwmiller)
The average of two numbers is 11. The difference between them is 4. Find the sum of the... (answered by Shin123,ikleyn)
Find two positive numbers such that the sum of the squares of the two numbers is 245 and... (answered by ikleyn,solver91311)
If the difference between two numbers is 6, and the difference of their squares is 180,... (answered by ewatrrr,MathLover1)
The sum of two numbers is 201 and the difference between them is 11. Find the two... (answered by richard1234)