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प्रश्न
At the end of the year 2016, the population of villages Kovad, Varud, Chikhali is 5x2 - 3y2, 7y2 + 2xy and 9x2 + 4xy respectively. At the beginning of the year 2017, x2 + xy - y2, 5xy and 3x2 + xy persons from each of the three villages respectively went to another village for education then what is the remaining total population of these three villages?
उत्तर
Total population of the three villages
= (5x2 - 3y2) + (7y2 + 2xy) + (9x2 + 4xy)
= 5x2 + 9x2 - 3y2 + 7y2 + 2xy + 4xy
= 14x2 + 4y2 + 6xy
Total number of persons who went to another village for education
= (x2 + xy - y2) + 5xy + (3x2 + xy)
= x2 + 3x2 - y2 + xy + 5xy + xy
= 4x2 - y2 + 7xy
∴ Remaining total population of the three villages = Total population of the three villages − Total number of persons who went to another village for education
= (14x2 + 4y2 + 6xy) - (4x2 - y2 + 7xy)
= 14x2 + 4y2 + 6xy - 4x2 + y2 - 7xy
= 14x2 - 4x2 + 4y2 + y2 + 6xy - 7xy
= 10x2 + 5y2 - xy
Thus, the remaining total population of these three villages is 10x2 + 5y2 − xy.
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