Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Lea solves the equation below by first squaring both sides of the equation.

3+2y=sqrt(-y)
What extraneous solution does Lea obtain?

y=

Lea solves the equation below by first squaring both sides of the equation. $\newline$ $3+2 y=\sqrt{-y}$ $\newline$ What extraneous solution does Lea obtain? $\newline$ $y=$

View step-by-step help

View step-by-step help

Evaluate recursive formulas for sequences

Full solution

Q. Lea solves the equation below by first squaring both sides of the equation.

\newline

3+2 y=\sqrt{-y}

\newline

What extraneous solution does Lea obtain?

\newline

y=

Perform Squaring: Now, let's perform the squaring on both sides. $\newline$ $(3 + 2y)^2 = -y$ $\newline$ $9 + 12y + 4y^2 = -y$
Move Terms: Next, we'll move all terms to one side to set the equation to zero. $\newline$ $4y^2 + 12y + y + 9 = 0$ $\newline$ $4y^2 + 13y + 9 = 0$
Solve Quadratic Equation: Now, we need to solve the quadratic equation for $y$ . We can use the quadratic formula, $y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a = 4$ , $b = 13$ , and $c = 9$ .
Calculate Discriminant: Let's calculate the discriminant $b^2 - 4ac$ first. $\newline$ Discriminant = $13^2 - 4(4)(9)$ $\newline$ Discriminant = $169 - 144$ $\newline$ Discriminant = $25$
Find Solutions: Since the discriminant is positive, we have two real solutions. Let's find them using the quadratic formula. $\newline$ $y = \frac{-13 \pm \sqrt{25}}{2 \times 4}$ $\newline$ $y = \frac{-13 \pm 5}{8}$
Check Validity: Now, let's find the two solutions. $\newline$ First solution: $y = (-13 + 5) / 8$ $\newline$ $y = -8 / 8$ $\newline$ $y = -1$ $\newline$ Second solution: $y = (-13 - 5) / 8$ $\newline$ $y = -18 / 8$ $\newline$ $y = -2.25$
Check Validity: Now, let's find the two solutions. $\newline$ First solution: $y = (-13 + 5) / 8$ $\newline$ $y = -8 / 8$ $\newline$ $y = -1$ $\newline$ Second solution: $y = (-13 - 5) / 8$ $\newline$ $y = -18 / 8$ $\newline$ $y = -2.25$ We have two potential solutions, $y = -1$ and $y = -2.25$ . However, we need to check these solutions in the original equation to see if any of them is extraneous. $\newline$ Original equation: $3 + 2y = \sqrt{-y}$
Check Validity: Now, let's find the two solutions. $\newline$ First solution: $y = (-13 + 5) / 8$ $\newline$ $y = -8 / 8$ $\newline$ $y = -1$ $\newline$ Second solution: $y = (-13 - 5) / 8$ $\newline$ $y = -18 / 8$ $\newline$ $y = -2.25$ We have two potential solutions, $y = -1$ and $y = -2.25$ . However, we need to check these solutions in the original equation to see if any of them is extraneous. $\newline$ Original equation: $3 + 2y = \sqrt{-y}$ Let's substitute $y = -1$ into the original equation. $\newline$ $y = -8 / 8$ $0$ $\newline$ $y = -8 / 8$ $1$ $\newline$ $y = -8 / 8$ $2$ $\newline$ This solution is valid.
Check Validity: Now, let's find the two solutions. $\newline$ First solution: $y = (-13 + 5) / 8$ $\newline$ $y = -8 / 8$ $\newline$ $y = -1$ $\newline$ Second solution: $y = (-13 - 5) / 8$ $\newline$ $y = -18 / 8$ $\newline$ $y = -2.25$ We have two potential solutions, $y = -1$ and $y = -2.25$ . However, we need to check these solutions in the original equation to see if any of them is extraneous. $\newline$ Original equation: $3 + 2y = \sqrt{-y}$ Let's substitute $y = -1$ into the original equation. $\newline$ $y = -8 / 8$ $0$ $\newline$ $y = -8 / 8$ $1$ $\newline$ $y = -8 / 8$ $2$ $\newline$ This solution is valid.Now, let's substitute $y = -2.25$ into the original equation. $\newline$ $y = -8 / 8$ $4$ $\newline$ $y = -8 / 8$ $5$ $\newline$ $y = -8 / 8$ $6$ $\newline$ This is not true, so $y = -2.25$ is an extraneous solution.

More problems from Evaluate recursive formulas for sequences

Question

Find the sum of the finite arithmetic series.

\sum_{n=1}^{10} (7n+4)

\newline

Posted 2 months ago

Question

Type the missing number in this sequence: `55,\59,\63,\text{_____},\71,\75,\79`

Posted 1 month ago

Question

Type the missing number in this sequence: `2, 4 8`, ______,`32`

Posted 2 months ago

Question

What kind of sequence is this?

2, 10, 50, 250, \ldots

Choices:Choices:

\newline

\text{[A]arithmetic}

\newline

\text{[B]geometric}

\newline

\text{[C]both}

\newline

\text{[D]neither}

Posted 2 months ago

Question

What is the missing number in this pattern?

1, 4, 9, 16, 25, 36, 49, 64, 81, \_\_\_\_

Posted 1 month ago

Question

Classify the series.

\sum_{n = 0}^{12} (n + 2)^3

\newline

\newline

\text{[A]arithmetic}

\newline

\text{[B]geometric}

\newline

\text{[C]both}

\newline

\text{[D]neither}

Posted 1 month ago

Question

Find the first three partial sums of the series.

\newline

1 + 6 + 11 + 16 + 21 + 26 + \cdots

\newline

Write your answers as integers or fractions in simplest form.

\newline

S_1 =

\newline

S_2 =

\newline

S_3 =

Posted 1 month ago

Question

Find the third partial sum of the series.

\newline

3 + 9 + 15 + 21 + 27 + 33 + \cdots

\newline

Write your answer as an integer or a fraction in simplest form.

\newline

S_3 =

Posted 1 month ago

Question

Find the first three partial sums of the series.

\newline

1 + 7 + 13 + 19 + 25 + 31 + \cdots

\newline

Write your answers as integers or fractions in simplest form.

\newline

S_1 =

\newline

S_2 =

\newline

S_3 =

Posted 2 months ago

Question

Does the infinite geometric series converge or diverge?

\newline

1 + \frac{3}{4} + \frac{9}{16} + \frac{27}{64} + \cdots

\newline

\newline

\text{[A]converge}

\newline

\text{[B]diverge}

Posted 1 month ago