00:00Let A, B, and C be non-zero real numbers.
00:02Given that A divided by 2 equals B divided by 3, which equals C divided by 5...
00:05We are asking which of the following ratios is equal to A cubed plus B cubed minus C cubed divided by A multiplied by B multiplied by C?
00:12That's your question, friends.
00:13Now, friends, A divided by 2 equals B divided by 3, which equals C divided by 5.
00:17I'll write it down right away.
00:18A divided by 2 is equal to B divided by 3 is equal to C divided by 5.
00:21That equality is equal to the proportionality K, isn't it, friends?
00:24Actually, even if you gave location A as 2, 3, or 5, you could still find the ratio in the same way.
00:30So what's the ratio, guys?
00:31It is independent of the proportionality constant K.
00:34But let's still consider the proportionality constant K to be equal.
00:38So, friends, what is a cube A?
00:40Here, A equals 2 times K.
00:42Right, guys?
00:44If A is cubed, then it is equal to 2 times K cubed, which equals 8K cubed.
00:50B equals 3 times K, so B cubed equals 3 times K cubed, which equals 27K cubed.
01:00We'll find it.
01:01Since C equals 5 times K, we take C cubed equals 5 times K cubed, and what do we get?
01:11We find it to be 125K cubed.
01:13Now let's move on to our ratio, folks.
01:15What is required of us?
01:16A cubed plus B cubed.
01:17Let's write it down right away.
01:18I write it as 8K cubed plus 27K cubed minus 125K cubed.
01:26That's what I'm saying, guys.
01:28A times B times C.
01:29So what's going on, guys?
01:302 times K times 3 times K times 5 times K.
01:34This equals, I say, my friends.
01:36What does 8K cubed plus 27K cubed make?
01:39If we add 35K cubed to minus 125K cubed, we get either 8K cubed or 125K cubed.
01:45If we remove them, what will we find them as?
01:53Of course, we find it to be minus 90K cubed.
01:57That's what I'm saying, guys.
01:582 times 3, 6 times 5, 30.
02:01Multiply by K cubed.
02:02We'll write the denominator here as well.
02:04Since the cubes in K are in a multiplication position, they cancel out.
02:07We find our answer as minus 3 in 91.30.
02:10That's what we're saying in the name of our answer, friends.
02:12Music
Yorumlar