Question 992486: Divide 16 into two parts such that the square of the bigger number is 64 more than the square of the smaller number. Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! We divide 16 into two parts/numbers: and , so that , and we say that = the bigger number, and = the smaller number.
It is not explicitly stated, but I suspect that the wording implies that and are both positive numbers, and probably positive integers.
The phrase "the square of the bigger number is 64 more than the square of the smaller number" translates as <---> .
Now we have a system of two equations: or .
From there, we can take different roads to the solution.
ONE WAY: --->--->--->--->--->--->--->--->--->
ANOTHER WAY: --->--->--->--->--->--->--->--->--->
A "CHEATING" WAY: <--->
A right triangle with legs measuring and has a hypotenuse measuring .
Look up a table of Pythagorean triples.
In that table you would find, in the first two columns, and (not necessarily in that order.
The third column will show .
In the first few rows you find two choices:
The first choice gives and shows you the solution.
The other row shows and has nothing to do with the solution.
