A^2 - b^2 = 2019 i need the answer to win a two dollar bet. both integers have to be positive

1 answer:

6 0

$Use\ a^2-b^2=(a-b)(a+b).\\\\a^2-b^2=2109\\\\(a-b)(a+b)=2019\\\\(a-b)(a+b)=3\cdot673\to a-b=3\ \wedge\ a+b=673\\\\\underline{+\left\{\begin{array}{ccc}a-b=3\\a+b=673\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2a=676\qquad\text{divide both sides by 2}\\.\qquad\boxed{a=338}\\\\\text{Put the value of a to the second equation}\\\\338+b=673\qquad\text{subtract 338 from both sides}\\\\\boxed{b=335}\\\\Answer:\ \boxed{a=338\ and\ b=335}$

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3 years ago

I need help with geometry. Find x.

I am Lyosha [343]

Answer:

Part 9) $x=5$

Part 10) $x=-9$

Step-by-step explanation:

we know that

The Midpoint Theorem states that: The segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side

Part 9) we know that

Point Q is the midpoint segment XY (QY=QX)

Point R is the midpoint segment XW (RW=RX)

Applying the Midpoint Theorem

RQ is parallel to WY

and

$RQ=\frac{1}{2}WY$