quadratic solving problems?

Question

One number is smaller than a second number. The sum of the squares of these numbers is 28 more than the product of the two numbers. Let x be the bigger number.
a. How will you represent the smaller number?
b. Represent the square of each number in terms of x.
c. Write the sum of the squares of the two numbers in terms of x.
d. Represent also the product of the two numbers in terms of x.
e. Write the equation and solve for x.
f. What is the bigger number?
g. What is the smaller number?

tnx..

Answer 1

a.let the smaller number be y.
b.the square of x in terms of x is : x^2
the square of y in terms of x is :
y=x+28-x^2
therefore y^2=(x+28-x^2) (x+28-x^2)
=56x-2x^3+784-55x^2+x^4
the square of y in terms of x is =
56x - 2x^3+784-55x^2+x^4
c. sum of the squares:
x^2+y^2=xy+28
x^2+(56x-2x^3+784-55x^2+x^4)=x.(x+28-x^2)+28
d. product of the two numbes:
xy=x^2+y^2-28
x.(x+28-x^2)=x^2+(56-2x^3+784-55x^2+x^4)-28
e. x=(y+28-y^2)^1/2
f. x is the bigger number = 6
g.y is the smaller number=4

Answer 2

1. Try y
3. x^2+y^2
4. xy
5. x^2+y^2= xy+28
6. x=6
7. y=4