330cm^3 = 6cm x 5cm x L
330^3 = 30cm^2 x L
L = 11cm
Because x,y,z form a geometric sequence, therefore the common ratio is
r = y/x = z/y
That is,
y² = xz (1)
We are given:
x + y + z = 18
Therefore
x + z = 18 - y (2)
Also,
x² + y² + z² = 612
Therefore, from (1), obtain
x² + z² + xz = 612
(x + z)² - xz = 612
From (1) and (2), obtain
(18 - y)² - y² = 612
324 - 36y + y² - y² = 612
-36y = 288
y = -8
Answer: y = -8
Hello there!
A C method : you multiply the A and C -> find the factors of AC that can add up to B. (a² + bx + c)
15a² + 14a - 8
you multiply 15 and -8 = -120
Find the two factors of -120 that adds up to 14.
We could used 20 and -6.
So we can split the original equation to this:
15a² + 20a - 6a - 8
Now, we use grouping method.
Let's group 15a² + 20a and -6a - 8.
15a² + 20a can be factored like this :
5a(3a + 4)
-6a - 8 can be factored like this :
-2(3a + 4)
So it is 5a(3a + 4) × -2(3a + 4)
We can simplify this into this :
(5a - 2)(3a + 4)
So your final answer is (5a - 2)(3a + 4).
Hope this helped! :)
