end of the year 2016 population of village kovad, varud and chikali is 5x^2-3y^2, 7y^2+2xy and 9x^2+4xy rrespectively. at the beginning of the year 2017 x^2+xy-y^2, 5xy and 3x^2+xy person from each village respectively went to another village for education then what is the remaining total population of these three villages?
Answers
Answer:
Total population of villages at the end of 2016 = (5x2 – 3y2) + (7y2 + 2xy) + (9x2 + 4xy) = 5x2 + 9x2 – 3y2 + 7y2 + 2xy + 4xy = 14x2 + 4y2 + 6xy …….(i) Total number of persons who went to other village at the beginning of 2017 = (x2 + xy – y2) + (5xy) + (3x2 + xy) = x2 + 3x2 – y2 + xy + 5xy + xy = 4x2 – y2 + 7xy … (ii) Remaining total population of villages = Total population at the end of 2016 – total number of persons who went to other village at the beginning of 2017 = 14x2 + 4y2 + 6xy – (4x2 – y2 + 7xy) … [From (i) and (ii)] = 14x2 + 4y2 + 6xy – 4x2 + y2 – 7xy = 14x2 – 4x2 + 4y2 + y2 + 6xy – 7xy = 1 = 10x2 + 5y2 – xy ∴ The remaining total population of the three villages is 10x2 + 5y2 – xy.Read more on Sarthaks.com - https://www.sarthaks.com/847028/the-end-the-year-2016-the-population-of-villages-kovad-varud-chikhali-is-5x-3y-7y-2xy-and-4xy
Answer:
10x² + 5y² - xy
Step by Step Explanation:
Total Population of three Villages:
= (5x² - 3y²) + (7y² + 2xy) + (9y² + 4xy)
= 5x² + 9x² - 3y² + 7 y² + 2xy + 4xy
= 14x² + 4y² + 6xy
Total Number of people who went into another village for education:
= (x² + xy - y²) + 5xy + (3x² + xy)
= x² + 3x² - y² + xy + 5xy + xy
= 4x² - y² + 7xy
Remaining total population of villagers=
Total Population of 3 Villages - Total Number of people who went into another village for education:
= (14x² + 4y² + 6xy) - (4x² - y² + 7xy)
= 14x² - 4x² + 4y² + y² + 6xy - 7xy
= 10x² + 5y² - xy