The demand equation for the Schmidt -3000 fax machine is 2x + p- 1,400=0 , where x is the quantity demanded per week and p is the unit price in dollars. The supply equation is 2x - 5p + 2,200=0, where is the quantity the supplier will make available in the market when the unit price is p dollars. Find the equilibrium quantity and the equilibrium price for the fax machines.

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lilyrockstarmag

01.08.2020

Mathematics

$\large\purple \dashrightarrow \pink{\frac{ \sqrt{2} + \sqrt{5} }{ \sqrt{2} - \sqrt{5} } }$

Multiply the fraction by $\frac{ \sqrt{2} + \sqrt{5} }{ \sqrt{2} + \sqrt{5} }$

$\large\purple \dashrightarrow \pink{\frac{ \sqrt{2} + \sqrt{5} }{ \sqrt{2} - \sqrt{5} } \times \frac{ \sqrt{2} + \sqrt{5} }{ \sqrt{2} + \sqrt{5} } }$

To multiply the fractions, multiply the numerators and denominators separately

$\large\purple \dashrightarrow \pink{\frac{( \sqrt{2} + \sqrt{5} ) \times ( \sqrt{2} + \sqrt{5} )}{( \sqrt{2} - \sqrt{5} ) \times ( \sqrt{2} + \sqrt{5} ) } }$

Write the repeated multiplication in exponential form

$\large\purple \dashrightarrow \pink{\frac{( \sqrt{2} + \sqrt{5} ) {}^{2} }{( \sqrt{2} - \sqrt{5} ) \times ( \sqrt{2} + \sqrt{5} ) } }$

Use (a-b)(a+b)=a²-b² to Simplify the denominator

$\large\purple \dashrightarrow \pink{\frac{( \sqrt{2} + \sqrt{5} ) {}^{2} }{ 2 - 5 }}$

Use (a+b)²=a²+2ab+b² to expand the numerator

$\large\purple \dashrightarrow \pink{\frac{ 2 + 2 \sqrt{10} + 5 }{ 2 - 5 }}$

Calculate the difference in denominator

$\large\purple \dashrightarrow \pink{\frac{ 2 + 2 \sqrt{10} + 5 }{ - 3}}$

Add the numbers in numerator

$\large\purple \dashrightarrow \pink{ - \frac{ 7 + 2 \sqrt{10} }{ 3}}$

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