Final answer:
The equation g² − 70 = 70 has two real solutions, which are g = √140 and g = -√140 after solving for g.
Step-by-step explanation:
The equation in question is g² − 70 = 70. To find out how many real solutions the equation has, we need to solve for g. First, we can add 70 to both sides of the equation to isolate g², giving us g² = 140. Taking the square root of both sides gives us g = ±√140. Since we are finding the real solutions, both positive and negative square roots are considered. Therefore, the equation has two real solutions: g = √140 and g = -√140.
The equation
�
2
−
70
=
70
g
2
−70=70 can be simplified to
�
2
=
140
g
2
=140 by adding 70 to both sides. To determine the number of real solutions, we can take the square root of both sides. However, it's important to note that there might be two solutions due to the positive and negative square roots.
The square root of 140 is approximately 11.83, so
�
g can be either
+
140
+
140
or
−
140
−
140
. Therefore, there are two real solutions to the equation:
�
=
140
g=
140
and
�
=
−
140
g=−
140
.
In summary, the equation
�
2
−
70
=
70
g
2
−70=70 has two real solutions. It is crucial to consider both the positive and negative roots when dealing with quadratic equations, as they represent valid solutions in the real number system.