Why does the equation 3x2 - 30 = 3 have two solutions but the equation 3x2 + 30 = 3 has no solution?
Try some different values for x.
The equation 3x^2 - 30 = 3 can be rewritten as 3x^2 = 33. Dividing both sides by 3 gives x^2 = 11. Taking the square root of both sides gives x = ±√11, which means there are two solutions.
On the other hand, the equation 3x^2 + 30 = 3 can be rewritten as 3x^2 = -27. Dividing both sides by 3 gives x^2 = -9. Taking the square root of both sides would give x = ±√(-9). However, the square root of a negative number is not a real number, so there is no real solution for x.
Trying different values for x:
- If we substitute x = 1 into the first equation, we get 3(1)^2 - 30 = 3 which is not true.
- If we substitute x = 1 into the second equation, we get 3(1)^2 + 30 = 3 which is also not true.
These calculations confirm that the first equation has no solution and the second equation has two solutions.