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Mademuasel [1]
3 years ago
9

What is the positive solution to the equation 0 = –x2 + 2x + 1?

Mathematics
1 answer:
Annette [7]3 years ago
7 0

The equation 0=-x^2+2x+1 is equivalent to the equation x^2-2x-1=0.

Solve this equation:

1. D=b^2-4ac=(-2)^2-4\cdot 1\cdot (-1)=4+4=8.

2. \sqrt{D}=\sqrt{8}=2\sqrt{2}.

3.

x_1=\dfrac{-b+\sqrt{D}}{2a}=\dfrac{2+2\sqrt{2}}{2}=1+\sqrt{2}

and

x_2=\dfrac{-b-\sqrt{D}}{2a}=\dfrac{2-2\sqrt{2}}{2}=1-\sqrt{2}.

4. Since \sqrt{2}>1, you have that 1-\sqrt{2}

Answer: the positive solution is x=1+\sqrt{2}.

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Find the oth term of the geometric sequence 7, 14, 28, ...
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