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mayasofia
16.01.2020 •
Mathematics
Two pools are being filled with water. to start, the first pool contains 1600 liters of water and the second pool contains 1339 liters of water. water is being added to the first pool at a rate of 25.25 liters per minute. water is being added to the second pool at a rate of 32.5 liters per minute.
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Ответ:
a)![\sqrt{61 - 24 \sqrt{5} } = - 4 + 3 \sqrt{5}](/tpl/images/0548/0811/1aeb0.png)
b)![( \sqrt{ ( {c}^{2} - 1) ({b}^{2} - 1) } - {2 \sqrt{bc} }) (\sqrt{ ( {c}^{2} - 1) ({b}^{2} - 1) } + {2 \sqrt{bc} } )](/tpl/images/0548/0811/c8916.png)
c)![\frac{ \sqrt{9 - 4 \sqrt{5} } }{2 - \sqrt{5} } = - 1](/tpl/images/0548/0811/64fd9.png)
Step-by-step explanation:
We want to simplify
Let :
Square both sides of the equation:
Expand the RHS;
Compare coefficients on both sides:
Solve the equations simultaneously,
Solve the quadratic equation in b²
This implies that:
When b=-3,
Therefore
We want to rewrite as a product:
as a product:
We rearrange to get:
We factor to get:
Factor again to get;
We rewrite as difference of two squares:
We factor the difference of square further to get;
c) We want to compute:
Let the numerator,
Square both sides of the equation;
Compare coefficients in both equations;
and
Put equation (2) in (1) and solve;
When b=-1, a=-2
This means that:
This implies that: