I don't understand how to do this

Mathematics

1 answer:

Elena-2011 [213]4 years ago

4 0

First, since both of the equations are equal to y you can set the equations equal to each other.
y=-2x +1
y=-2x^2 + 3x +1

-2x + 1= -2x^2 + 3x + 1

Second, add 2x^2 and subtract 3x and 1 from both sides.
-2x + 1 = -2x^2 + 3x + 1
-3x -1 +2x^2 +2x^2 -3x -1
________________
2x^2 - 5x = 0

Third, factor out an x.
x(2x - 5) = 0

Fourth, solve for x by setting each factor equal to 0.

x= 0 2x-5=0
+5 +5
_______
2x = 5
---- ----
2 2
________
x=5/2

So the values of x that satisfy the system of equations is 0 and 5/2.

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Multiply (sqrt 10 + 2 sqrt 8) (sqrt 10 -2 sqrt 8)

sveta [45]

$(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) = -22$

Solution:

Given that we have to multiply the given expression

Given is:

$(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8})$

We have to multiply the above expression

Apply the difference of two squares formula

$(a+b)(a-b) = a^2-b^2$

Similarly for,

$(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8})$

We have,

$a = \sqrt{10}\\\\b = 2\sqrt{8}$

Thus the equation becomes,

$(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) = (\sqrt{10})^2 - (2\sqrt{8})^2\\\\Simplify\\\\(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) =(\sqrt{10} \times \sqrt{10}) - (2\sqrt{8} \times 2\sqrt{8})$

Use the below rule,

$\sqrt{a} \times \sqrt{a} = a$

Therefore, the above equation becomes,

$(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) =10 - 4 \times 8\\\\(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) = 10 - 32\\\\(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) =-22$