Question 898355: The difference of two numbers is 7 and the sum of their squares is 137.
Find the numbers.
The sum of two numbers is 8; the square of the first minus twice the
square of the second equals 7. Find them.
Find two numbers that differ by 8 and whose product is 273.
There is a rectangle whose perimeter is 46 meters and whose area is
112 square meters. What are its dimensions?
The sum of the areas of two squares is 325 square meters. The side of
one increased by the side of the other is 25 meter. Find the length of a
side of each.
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! The difference of two numbers is 7 and the sum of their squares is 137.
Find the numbers.
(x-y)=7
(x-y)^2=49
x^2+y^2= 137
(x-y)^2+2xy = 137
7^2+2xy=137
2xy= 137-49
2xy=88
xy=44
x-y=7
x=44/y
44/y -y = 7
44-y^2= 7y
y^2+7y-44=0
y^2+11y-4y-44=0
y(y+11)-4(y+11)=0
(y+11)(y-4)=0
y=-11 OR 4
x-y=7
if y=-11
x+11=7
x=-4
(-11, -4)
if y=4
x=11
(11,4)
The sum of two numbers is 8; the square of the first minus twice the
square of the second equals 7. Find them.
one number be x
other number = (8-x)
x^2-2(8-x)^2=7
x^2-2(64-16x+x^2)=7
x^2-128+32x-2x^2=7
-x^2+32x-135=0
x^2-32x+135=0
x^2-27x-5x+135=0
x(x-27)-5(x-27)=0
(x-27)(x-5)=0
x=5 OR 27
xnot equal to 27
x= 5
(5,2)
Find two numbers that differ by 8 and whose product is 273.
x & 8+x
x(8+x)=273
8x+x^2=273
x^2+8x -273=0
x^2+21x-13x-273=0
x(x+21)-13(x+21)=0
(x+21)(x-13)=0
x=-21 OR 13
There is a rectangle whose perimeter is 46 meters and whose area is
112 square meters. What are its dimensions?
The sum of the areas of two squares is 325 square meters. The side of
one increased by the side of the other is 25 meter. Find the length of a
side of each.
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