SOLUTION: The larger of two numbers is 5 more than twice the smaller. The square of the smaller is equal to the larger. Find the numbers

Question 390980: The larger of two numbers is 5 more than twice the smaller. The square of the smaller is equal to the larger. Find the numbers
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

let larger number be and smaller number
if the larger of is {{5}}} more than twice the smaller number, we have:
..........(1)
if the square of the smaller is equal to the larger,we have
.........(2)
solve the system:
..........(1)
.........(2).......substitute in (1)
-----------------------------

..........(1).solve for

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=-2, and c=-5

Negate -2 to get 2

Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So the solutions are:

or

..................................

...................................
find

check:

..........(1)...plug in and

.........(2)....plug in and

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