Please help with this.<br> thanks sm!

Prove that if a and b are integers, then a^2-4b egal or non-egal 2

Lera25 [3.4K]

Answer:

tex]a^2 - 4b \neq 2[/tex]

Step-by-step explanation:

We are given that a and b are integers, then we need to show that $a^2 - 4b \neq 2$

Let $a^2 - 4b = 2$

If a is an even integer, then it can be written as $a = 2c$ , then,

$a^2 - 4b = 2\\(2c)^2 - 4b =2\\4(c^2 -b) = 2\\(c^2 -b) =\frac{1}{2}$

RHS is a fraction but LHS can never be a fraction, thus it is impossible.

If a is an odd integer, then it can be written as $a = 2c+1$ , then,

$a^2 - 4b = 2\\(2c+1)^2 - 4b =2\\4(c^2+c-b) = 2\\(c^2+c-b) =\frac{1}{4}$

RHS is a fraction but LHS can never be a fraction, thus it is impossible.

Thus, our assumption was wrong and $a^2 - 4b \neq 2$ .

7 0

3 years ago

The sampling distribution used when making inferences about a single population variance is?

melamori03 [73]

We use the chi-square distribution when making inferences about a single population variance.

Short Description of Chi-Square Distribution

The continuous probability distribution known as the chi-square distribution. The number of degrees of freedom (k) a chi-square distribution has determines its shape. This type of sampling distribution has a variance of 2k and a mean equal to its number of degrees of freedom (k). The range is of a chi-square distribution is from 0 to ∞.

Variance plays a key role in the analysis of risk and uncertainty. The sample variance, an unbiased estimator of population variance, is expressed by the following formula of core statistic for a sample size 'n' and Y' as the sample mean:

S² = ∑(Yₓ - Y') / (n-1)

The formula, (n-1)S² / σ² has the central chi-square distribution as χ²ₙ₋₁. Here (n-1) represents the degrees of freedom.

Learn more about chi-square distribution here:

brainly.com/question/13857280

#SPJ1

4 0

1 year ago

The product of the square of a number x and 2 subtracted from 3 is y.

lozanna [386]

The algebraic expression for the given statement is: 2x² - 3 = y.

<h3>How to Write an Algebraic Expression?</h3>

To wrote an algebraic expression is translate a statement using numbers, variables, and mathematical sign into a mathematical statement.