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Karolina [17]
3 years ago
5

Use the identity (x+y)(x2−xy+y2)=x3+y3 to find the sum of two numbers if the product of the numbers is 28, the sum of the square

s is 65, and the sum of the cubes of the numbers is 407.
Mathematics
2 answers:
fgiga [73]3 years ago
4 0

Answer:

Step-by-step explanation:

1) f(x) = x+y , xy = 49 --> f(x) = x+49/x

f '(x) = 1-49/x2 , x = ±√49 , choose x = +7

y = 49/x = 7

smaller = 7

larger = 7

2) Vertical Distance is difference between the two functions

V(x) = x+56 - x2, V '(x) = 1 -2x --> x = 1/2 --> V(1/2) = 56.25 <---Max Vertical distance

Boundary at -7 and 8 are less

3) I googled the equation, it is really y(n) = kn/(49+n2)

y '(n) = (k(49+n2) - 2kn2)/(49+n2) , Setting to zero, k(49+n2) -2kn2 = 0 , n = 7

4) Let x and y be the sides of the rectangle. A = xy = 37.5 Million or y = 37.5/x

The length of the fences is f(x) = 2x + 3y = 2x+112.5/x

f '(x) = 2-112.5/x2 --> x = √56.5 = 7.5 and y = 37.5/7.5 = 5 then scale by √Million

smaller = 5000 ft and larger = 7500 ft

this took me ages to work out so hopefully it helped

yanalaym [24]3 years ago
3 0

Answer:

x + y = 11

Step-by-step explanation:

xy = 28

x² + y² = 65

x³ + y³ = 407

(x + y)(x² - xy + y²) = x³ + y³

(x + y)(x² + y² - xy) = x³ + y³

(x + y)(65 - 28) = 407

37(x + y) = 407

x + y = 407÷37

x + y = 11

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