SOLUTION: A positive number is divided into two parts such that the squares of the two parts is 20. The square of the larger number is 8 times the smaller number. Take the smaller number as

Question 991845: A positive number is divided into two parts such that the squares of the two parts is 20. The square of the larger number is 8 times the smaller number. Take the smaller number as x.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x is the smaller number.
y is the larger number.
x^2 + y^2 = 20
you are given that the square of the larger number is equal to 8 time the smaller number.
that gets you y^2 = 8x.
rpelace y^2 with 8x in the original equation to get:
x^2 + 8x = 20
subtract 20 from both sides of the equation to get:
x^2 + 8x - 20 = 0
factor this quadratic equation to get:
(x+10) * (x-2) = 0
solve for x to get:
x = -10 and x = 2
since x has to be positive, you get x = 2 as your potential solution.
when x = 2, y^2 = 8x = 16.
this makes y = 4
your solution is that x = 2 and y = 4
x^2 + y^2 = 20 becomes 2^2 + 4^2 = 20 which becomes 4 + 16 = 20 which becomes 20 = 20.
this confirms the values are good.
you get:
x = 2 and y = 4 as your solution.

RELATED QUESTIONS
A positive number is divided into two parts such that the sum of the squares of the two... (answered by Edwin McCravy)

a positive number is divided into two parts such that the sum of the squares of the two... (answered by ankor@dixie-net.com)

The number 15 is divided into two integral parts such that times the square of the... (answered by Alan3354)

The number 77 is divided into two parts such that H.C.F of two parts is 11 and their... (answered by MathTherapy)

A number is divided into two parts, such that one part is 12 more than the other. If the... (answered by ikleyn)

A number is divided into two parts, such that one part is 12 more than the other. If the... (answered by Theo,ikleyn,greenestamps)

Separate 30 into two parts such that one number is one-fourth of the... (answered by ptaylor)

divide 182 meters into two parts such that the smaller is 1/13 of the larger (answered by josgarithmetic,greenestamps)

The number 40 is divided into two parts in such way that two times the square of the... (answered by greenestamps)