Two numbers differ by 9. The sum of their squares is 653. Find the numbers.

Question

anonymous · Answer

Please help me.

raden · Answer

x-y=9 ---> x=y+9
x^2 + y^2 = 653
(y+9)^2 + y^2 = 653
2y^2 + 18y + 81 -653 = 0
2y^2 + 18y + 81 -572 = 0
y^2 + 9y - 286 = 0
(y+22)(y-13)=0
y=13
x=y+9=13+9=22

anonymous · Answer

Thanks! Such a big help.

raden · Answer

welcome

raden · Answer

wait, each numbers must be positive or may a negative numbers ?

anonymous · Answer

They are all positive.

raden · Answer

ok, it think that's all cleared

anonymous · Answer

Can you help me again this one is pretty hard for me.
 
The length of a rectangle is 3cm longer than twice its width. The area is 119 square centimeters. What are the dimensions of the rectangle?

raden · Answer

l = 2w+3
A = 119
l*w = 119
(2w+3)w =119
2w^2 +3w -119 = 0
(2w + 17)(w - 7) = 0
w = 7 cm
so, l = 2w+3 = 2(7)+3 = 17

raden · Answer

the dimensions of the rectangle :  17 x 7

anonymous · Answer

Genius! Thanks again!

raden · Answer

but, sometimes :p