First of all, let's focus on the first condition given by the ennunciation, namely 5x-11y = 2x+5y.
We'll group the term in "x" into the left side of the equal and the terms in "y" into the right side and we'll do the math:
5x-2x = 11y+5y
3x=16y
For the moment, let's stop in this point of action.
Now,l let's focus on the exression which we have to calculate:
(3x² + 2y²) : (3x² - 2y²)
The expression at numerator, (3x² + 2y²), we could re-write it in this way:
(3x² + 2y²)= (3x + 2y)² - 2*3x*2y
The expression at denominator, (3x² - 2y²), is a difference ofsquares and it could be written as:
(3x² - 2y²)= (3x - 2y)*(3x + 2y)
Now, let's put together the found expressions:
(3x² + 2y²) : (3x² - 2y²)= [(3x + 2y)² - 2*3x*2y]/(3x - 2y)*(3x + 2y)
In the end, let's turn back at the found condition:
3x=16y
We'll apply some tricks on this condition, depending on the last form of the expression which we have to calculate:
3x=16y
3x + 2y=16y+2y
3x + 2y=18y
3x - 2y=16y-2y
3x - 2y=14y
Now, all we have to do is to substitute the calculated expressions above, into our expression:
[(3x + 2y)² - 2*3x*2y]/(3x - 2y)*(3x + 2y)=[(18y)²- 2*16y*2y]/(14y)*(18y)
[(18y)²- 2*16y*2y]/(14y)*(18y)=[(18y)²-2²*4²*y²]/14*18*y²=
But, at the numerator we have again a difference of squares:
[(18y)²-2²*4²*y²]=(18y-8y)(18y+8y)=10y*26y
[(18y)²-2²*4²*y²]/14*18*y²=10y*26y/14*18*y²
10y*26y/14*18*y²=2*5*2*13*y²/2*7*2*9*y²
After simplifying:
3x² + 2y² : 3x² - 2y²=65/63
No comments:
Post a Comment