The sum of twice a triangular number x and its subscript is 24. If their difference is 6, find x..
Triangular numbers are numbers of the form: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91...
The x-th triangular number (the triangular number which has x as its subscript) is:
T(x) = 1 + 2 + 3 + ... + x
Which we can also write as:
T(x) = x*(x+1)/2
So to answer our question we have to solve the following equation:
2*T(x) + x = 24
Which, after rewriting using the aforementioned formula, ultimately yields the quadratic equation:
x² + 2*x - 24 = 0
With x = 4 as its only positive root.
Note that we didn't need the condition on the difference between the two numbers, but our solution indeed satisfies it, in fact we have x = 4 and so T(x) = 10, and 10 - 4 = 6.
by Grace Marguerite Williams 7 years ago
How is the culture of the large family differ from that of the small family?
by Nathan Bernardo 6 years ago
Is there a difference between judgment and perception? If so, what is the difference?In addition, can perception and action occur simultaneously. Does the difference, therefore, between judgment and perception have something to do with time?
by Myn Is Me 6 years ago
How does the Indian Elephant differ from the African Elephant?
by pedagog 6 years ago
What is the main reason for great difference between average life-span of different mammals? for common house mouse:4, for Norway rat :7, for dogs: 29, for cats:38, for polar bears:42, for horses:62, for...
by Liz Elias 2 months ago
Okay, there is a trick to this one; you must think outside the box. (Remember, I'm not a mathematician, and I suck at math...so this is more of a creative thinking than a math quiz.)What is the sum of the 1st G, squared?
by mbarbosa3 8 years ago
Karin said eleven more than my number is the same as 18 more than twice my number what is karins...number
|HubPages Device ID|
|Login||This is necessary to sign in to the HubPages Service.|
|HubPages Google Analytics|
|HubPages Traffic Pixel|
|Google Hosted Libraries|
|Google AdSense Host API|
|Conversion Tracking Pixels|
|Author Google Analytics|
|Amazon Tracking Pixel|