Answer:
the product of the 2 numbers is 22
Step-by-step explanation:
x² + y² = 80
(x - y)² = 36
=>
x - y = 6
or y - x = 6
let's start with the first one x-y=6
x = 6 + y
=>
(6+y)² + y² = 80
y² + 6y +6y + 36 + y² = 80
2y² + 12y + 36 = 80
2y² + 12y - 44 = 0
y² + 6y - 22 = 0
the solution of a quadratic equation
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case here we have an squadron in y.
a=1
b=6
c=-22
(-6 ± sqrt(36 + 4×22))/2 = (-6 ± sqrt(36+88))/2 =
= (-6 ± sqrt(124))/2 = (-6 ± sqrt(4×31))/2 =
= (-6 ± 2×sqrt(31))/2 = -3 ± sqrt(31)
y1 = -3 + sqrt(31)
y2 = -3 - sqrt(31)
=>
x1 = 6 + -3 + sqrt(31) = 3 + sqrt(31)
x2 = 3 - sqrt(31)
control :
(-3 + sqrt(31))² + (3 + sqrt(31))² = 80
9 - 3 sqrt(31) - 3 sqrt(31) + 31 + 9 +3 sqrt(31) + 3 sqrt(31) + 31 = 80
9 + 31 + 9 +31 = 80
18 + 62 = 80
80 = 80 correct
solving now for y-x=6
delivers exactly the same calculations, just with x and y trading places.
so, the resulting 2 number pairs are the same.
the product of the 2 numbers :
(3 + sqrt(31))(-3 + sqrt(31)) = -9 - 3 sqrt(31) + 3 sqrt(31) + 31 =
= -9 + 31 = 22
(3 - sqrt(31))(-3 - sqrt(31)) = -9 + 3 sqrt(31) - 3 sqrt(31) + 31 =
= 22
so, the product is the same in both cases.
is used to convert from inches to cm. The inches unit in the denominator cancels with one of the inches unit from the original 112 square inches figure.
, as "inches times inches". Or think of a 1 inch by 1 inch square that has an area of 1 square inch. The same applies for the square centimeter unit as well.
