Answer:
x=
−
2
+
3
√
5
y=
3
√
5
Step-by-step explanation:
Positive real number =
x
Other number =
y
First statement: A positive real number is 2 less than another.
Therefore
y
=
x
+
2
Second statement: When 4 times the larger is added to the square of the smaller, the result is 49.
Since the larger number is
y
, we know that "4 times the
larger" means
4
y
.
The square of the smaller would mean
x
2
.
If you put them together, it would look like
4
y
+
x
2
=
49
.
Now create a system of equations like the following:
y
=
x
+
2
4
y
+
x
2
=
49
.
From the first equation, we can understand the value of
y
in terms of
x
, which is
x
+
2
.
Replace the
y
in the second equation with
x
+
2
.
4
(
x
+
2
)
+
x
2
=
49
Now that we have an equation with only one variable, solve for
x
.
Below is a potential way one can solve this equation:
1. Expand the bracket.
4
x
+
8
+
x
2
=
49
2. Form a quadratic equation (
a
x
2
+
b
x
+
c
=
0
)
x
2
+
4
x
−
41
=
0
3, Use
−
b
±
√
b
2
−
4
a
c
2
(
a
is 1,
b
is 4,
c
is -41.)
−
4
±
√
4
2
−
4
⋅
(
−
41
)
2
−
4
±
(
180
)
1
2
2
−
2
±
3
√
5
Since the answer must be a positive real number,
x
will be
−
2
+
3
√
5
If you place
−
2
+
3
√
5
into
y
=
x
+
2
:
y
=
−
2
+
3
√
5
+
2
You will get
3
√
5
for
y
.
