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)
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
