Question

x(x-1)/2 = 25(49) - x(x-1)/2
find X ​

Answer 1

Answer:

What is the solution to x^2+y^2=25, xy=12?

So we are given 2 equations:

x2+y2=25

xy=12

And wish to find all possible solutions for this. Let us start by using the second equation and solving for y:

y=12x

Which gives:

x2+144x2=25

Throw around some numbers:

x2−25=−144x2

x4−25x2=−144

x4−25x2+144=0

So, complete the square to solve for x:

(x2−252)2−6254+144=0

(x2−252)2=6254−5764

(x2−252)2=494

x2−252=±72

x2=252±72

x2=25+72 or x2=25−72

x2=9 or x2=16

Since the highest polynomial is a grade four, this means four solutions, ±3 and ±4 . Plugging this in to the second equation, we finally get the four points:

(3,4) , (−3,−4) , (4,3) and (−4,−3) .

And with that, the answer can be simplified to ±(3,4) and ±(4,3) .