Solve the following problems

If $x + y = a x^{2} + y^{2} = b^{2}$ and $x^{3} + y^{3} = c^{3}$ then show that $a^{3} + 2 c^{3} = 3 a b^{2}$

Created: 3 months ago | Updated: 2 months ago

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Here,

$L . H . S = a^{3} + 2 c^{3} = (x + y)^{3} + 2 (x^{3} + y^{3})$

$= x^{3} + y^{3} + 3 x^{2} * y + 3 x * y^{2} + 2 x^{3} + 2 y^{3}$

$= 3 x^{3} + 3 y^{3} + 3 x^{2} y + 3 x y^{2}$

$= 3 (x^{3} + y^{3}) + 3 x y (x + y)$

$= 3 (x + y) (x^{2} - x y + y^{2}) + 3 x y (x + y)$

$= 3 (x + y) (x^{2} - x y + y^{2} + x y)$

$= 3 (x + y) (x^{2} + y^{2}) = 3 a b^{2}$

= R.H.S (Proved)

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Two men and three women completed only one fourth portion of a job in 3 days. After 3 days, another man was included in the team and two days they completed another one fourth portion of the job. How many men (with no women) can complete the whole job in 4 days?

Created: 3 months ago | Updated: 2 months ago

Job Solution One Bank Ltd ONE Bank Ltd. || SCO Examination (29-06-2018) || 2018 গণিত

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In 2017, the number of pairs of the shoes that a company sold to retailers decreased by 20%, while the price per pair increased by 20% from that of the previous year. Company's revenue from the sales of the shoes in 2017 was Tk 6,00,000. Find out the difference between the sales revenue of the year 2017 and 2016?

Created: 3 months ago | Updated: 2 months ago

Job Solution One Bank Ltd ONE Bank Ltd. || SCO Examination (29-06-2018) || 2018 গণিত

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A sum of money is to be distributed equally among a group of children. If there were 25 children less then each would get Tk. 1.50 more, and if there were 50 children more, each would get Tk. 1.50 less. Find the number of children and the amount of money distributed.

Created: 3 months ago | Updated: 2 months ago

Job Solution One Bank Ltd ONE Bank Ltd. || SCO Examination (29-06-2018) || 2018 গণিত

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Solve the equation: $\frac{x + 3}{x + 2} - \frac{x - 4}{x + 3} = \frac{x + 5}{x + 4} - \frac{x + 6}{x + 5}$

Created: 3 months ago | Updated: 2 months ago

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Salam used part of Tk. 100,000 to purchase a television. Of the remaining portion, he invested 1/3 of it at 4 percent simple annual interest and 2/3 it at 6 percent simple annual interest, if after a year the income from the two investments totaled Tk 320, what was the purchase price of the television?

Created: 3 months ago | Updated: 2 months ago

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Solve the following problems

If x+y=ax2+y2=b2 and x3+y3=c3 then show that a3+2c3=3ab2

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Two men and three women completed only one fourth portion of a job in 3 days. After 3 days, another man was included in the team and two days they completed another one fourth portion of the job. How many men (with no women) can complete the whole job in 4 days?

A sum of money is to be distributed equally among a group of children. If there were 25 children less then each would get Tk. 1.50 more, and if there were 50 children more, each would get Tk. 1.50 less. Find the number of children and the amount of money distributed.

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