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3 years ago

What is the solución of the equation x2-4x+1=0?

Mathematics

1 answer:

koban [17]3 years ago

6 0

Answer:

x = 2 + √3 and

x = 2 - √3

Step-by-step explanation:

Please use " ^ " to denote exponentiation: x^2 - 4x + 1 = 0.

Here you have multiple choices of methods of solution:

quadratic formula, completing the square, graphing, and so on.

If we complete the square, then: x^2 - 4x + 1 = 0 becomes

x^2 - 4x + 4 - 4 + 1 = 0, or

(x - 2)^2 = 3

Taking the square root of both sides, we get x - 2 = ±√3, so that the roots are:

x = 2 + √3 and

x = 2 - √3

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Three fourths a number plus 8 is 20 less than the number

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Answer:

Equation: $\frac{3}{4}n+8=n-20$

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Step-by-step explanation:

To first set up the equation, you need to look at the verbal description and translate into numbers and operations:

'three fourths a number' = $\frac{3}{4} n$

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Put the expressions together:

'three fourths a number plus 8': $\frac{3}{4}n+8$

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Set them equal to each other and solve: $\frac{3}{4}n+8=n-20$

Add 20 to both sides: $\frac{3}{4}n+8+20=n-20+20$

Subtract $\frac{3}{4}n$ from both sides: $\frac{3}{4}n-\frac{3}{4}n+28=n-\frac{3}{4}n$

Multiply both sides by $\frac{4}{1}$ : $\frac{4}{1}28=\frac{1}{4}n\frac{4}{1}$

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