4. 3h² - 147 = 0 p√t = √x t = x
Answer (1)
Let's solve the quadratic equation given by the expression 3 h 2 − 147 = 0 .
Step-by-Step Solution:
Identify the Standard Form : The equation 3 h 2 − 147 = 0 is already in the standard quadratic form a x 2 + b x + c = 0 , where a = 3 , b = 0 , and c = − 147 .
Simplify the Equation : Start by isolating the h 2 term:
3 h 2 = 147
Divide both sides by 3 to solve for h 2 :
h 2 = 3 147
h 2 = 49
Find the Square Root : To find h , take the square root of both sides:
h = ± 49
h = ± 7
Conclusion:
The solutions to the equation are h = 7 and h = − 7 . This means the values of h that satisfy the equation 3 h 2 − 147 = 0 are 7 and -7. The solution process involves solving a basic quadratic equation using square roots, making this an appropriate question for high school mathematics.
