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mario62 [17]
3 years ago
14

Sviatoslav solved the quadratic equation x^2-x-1=0 by completing the square. In the process, he came up with the equivalent equa

tion (x+a)^2 = b, where a and b are constants. What is b?
Mathematics
1 answer:
zimovet [89]3 years ago
6 0

Answer:

x=\frac{1+\sqrt5}{2} and  x=\frac{1-\sqrt5}{2}

and b=\frac{5}{4}

Step-by-step explanation:

We are given that a quadratic equation

x^2-x-1=0

We have to solve the equation by completing square and find the value of b.

(x)^2-2\times x\times \frac{1}{2}+(\frac{1}{2})^2-(\frac{1}{2})^2-1=0

(x-\frac{1}{2})^2-\frac{1}{4}-1=0

(x-\frac{1}{2})^2-\frac{1-4}{4}=0

(x-\frac{1}{2})-\frac{5}{4}=0

(x-\frac{1}{2})^2-(\frac{\sqrt5}{2})^2=0

(x-\frac{1}{2})^2=(\frac{\sqrt5}{2})^2

x-\frac{1}{2}=\frac{\sqrt5}{2} and x-\frac{1}{2}=-\frac{\sqrt5}{2}

x=\frac{\sqrt5}{2}+\frac{1}{2}=\frac{1+\sqrt5}{2}

And x=\frac{1}{2}-\frac{\sqrt5}{2}=\frac{1-\sqrt5}{2}

Therefore,x=\frac{1+\sqrt5}{2} and  x=\frac{1-\sqrt5}{2}

and b=\frac{5}{4}

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