6
Solution:
√36 - x^2 = 336 - x^2 = 3^236 - x^2 = 9x^2 = 27x = ±√27
√7 - x^2 = √-6x7 - x^2 = -6xx^2 - 6x - 7 = 0(x-7)(x+1) = 0x = 7 or x = -1
(2x-3)√(2x^2-5x+2) = 0Setting each factor equal to zero:2x - 3 = 02x = 3x = 3/2
√(2x^2 - 5x + 2) = 02x^2 - 5x + 2 = 0(2x-1)(x-2) = 0x = 1/2 or x = 2
Combining the solutions, we have x = 3/2, 1/2, 2.
Therefore, 12 * 2 = 24.
6
Solution:
√36 - x^2 = 3
36 - x^2 = 3^2
36 - x^2 = 9
x^2 = 27
x = ±√27
√7 - x^2 = √-6x
7 - x^2 = -6x
x^2 - 6x - 7 = 0
(x-7)(x+1) = 0
x = 7 or x = -1
(2x-3)√(2x^2-5x+2) = 0
Setting each factor equal to zero:
2x - 3 = 0
2x = 3
x = 3/2
√(2x^2 - 5x + 2) = 0
2x^2 - 5x + 2 = 0
(2x-1)(x-2) = 0
x = 1/2 or x = 2
Combining the solutions, we have x = 3/2, 1/2, 2.
∛144 ∛(4 √9)∛144 = 2∛36 = 26 = 12
∛(4 3) = ∛12 = 2
Therefore, 12 * 2 = 24.