You can
put this solution on YOUR website!"The difference of two positive numbers is 5" means that
(note: this means that
)
Also, because "the sum of their squares is 157" we know that
Start with the first equation.
Subtract x from both sides.
Multiply both sides by -1 and rearrange the terms.
Move onto the second equation.
Plug in
FOIL
Subtract 157 from both sides.
Combine like terms.
Notice that the quadratic
is in the form of
where
,
, and
Let's use the quadratic formula to solve for "x":
Start with the quadratic formula
Plug in
,
, and
Negate
to get
.
Square
to get
.
Multiply
to get
Rewrite
as
Add
to
to get
Multiply
and
to get
.
Take the square root of
to get
.
or
Break up the expression.
or
Combine like terms.
or
Simplify.
So the possible solutions are
or
However, it's stated that the numbers are positive. So the only answer is
Now just plug that value into
and solve for 'y' to get
--->
So the two numbers are
and
Notice how 11-6=5. So their difference is 5
Also, take note how
.
So this confirms our answer.
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