Question Find the conjugate of $7-\sqrt{x+3}$ when $x \geq -3$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the expression $7 - \sqrt{x+3}$ .
2. We need to find the conjugate of the given expression.
3. The domain for $x$ is $x \geq -3$ .

STEP 2

The conjugate of a binomial expression of the form $a + b$ is $a - b$ , and the conjugate of $a - b$ is $a + b$ . The purpose of finding a conjugate is often to rationalize a denominator or to simplify an expression.

STEP 3

Identify the terms in the given expression that will be involved in the conjugate. In this case, the expression is $7 - \sqrt{x+3}$ , so the terms are $7$ and $-\sqrt{x+3}$ .

STEP 4

Write the conjugate of the given expression by changing the sign between the two terms. Since the original expression is $7 - \sqrt{x+3}$ , the conjugate will be $7 + \sqrt{x+3}$ .

STEP 5

The conjugate of the expression $7 - \sqrt{x+3}$ when $x \geq -3$ is $7 + \sqrt{x+3}$ .
The solution is $7 + \sqrt{x+3}$ .

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Question Find the conjugate of $7-\sqrt{x+3}$ when $x \geq -3$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the expression $7 - \sqrt{x+3}$ .
2. We need to find the conjugate of the given expression.
3. The domain for $x$ is $x \geq -3$ .

STEP 2

The conjugate of a binomial expression of the form $a + b$ is $a - b$ , and the conjugate of $a - b$ is $a + b$ . The purpose of finding a conjugate is often to rationalize a denominator or to simplify an expression.

STEP 3

Identify the terms in the given expression that will be involved in the conjugate. In this case, the expression is $7 - \sqrt{x+3}$ , so the terms are $7$ and $-\sqrt{x+3}$ .

STEP 4

Write the conjugate of the given expression by changing the sign between the two terms. Since the original expression is $7 - \sqrt{x+3}$ , the conjugate will be $7 + \sqrt{x+3}$ .

STEP 5

The conjugate of the expression $7 - \sqrt{x+3}$ when $x \geq -3$ is $7 + \sqrt{x+3}$ .
The solution is $7 + \sqrt{x+3}$ .

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Question Find the conjugate of 7−x+37-\sqrt{x+3}7−x+3​ when x≥−3x \geq -3x≥−3.

Studdy Solution

STEP 1

Assumptions1. We are given the expression 7−x+37 - \sqrt{x+3}7−x+3​.2. We need to find the conjugate of the given expression.3. The domain for xxx is x≥−3x \geq -3x≥−3.

STEP 2

The conjugate of a binomial expression of the form a+ba + ba+b is a−ba - ba−b, and the conjugate of a−ba - ba−b is a+ba + ba+b. The purpose of finding a conjugate is often to rationalize a denominator or to simplify an expression.

STEP 3

Identify the terms in the given expression that will be involved in the conjugate. In this case, the expression is 7−x+37 - \sqrt{x+3}7−x+3​, so the terms are 777 and −x+3-\sqrt{x+3}−x+3​.

STEP 4

Write the conjugate of the given expression by changing the sign between the two terms. Since the original expression is 7−x+37 - \sqrt{x+3}7−x+3​, the conjugate will be 7+x+37 + \sqrt{x+3}7+x+3​.

STEP 5

The conjugate of the expression 7−x+37 - \sqrt{x+3}7−x+3​ when x≥−3x \geq -3x≥−3 is 7+x+37 + \sqrt{x+3}7+x+3​.The solution is 7+x+37 + \sqrt{x+3}7+x+3​.

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Question Find the conjugate of $7-\sqrt{x+3}$ when $x \geq -3$ .

Assumptions
1. We are given the expression $7 - \sqrt{x+3}$ .
2. We need to find the conjugate of the given expression.
3. The domain for $x$ is $x \geq -3$ .

The conjugate of a binomial expression of the form $a + b$ is $a - b$ , and the conjugate of $a - b$ is $a + b$ . The purpose of finding a conjugate is often to rationalize a denominator or to simplify an expression.

Identify the terms in the given expression that will be involved in the conjugate. In this case, the expression is $7 - \sqrt{x+3}$ , so the terms are $7$ and $-\sqrt{x+3}$ .

Write the conjugate of the given expression by changing the sign between the two terms. Since the original expression is $7 - \sqrt{x+3}$ , the conjugate will be $7 + \sqrt{x+3}$ .

The conjugate of the expression $7 - \sqrt{x+3}$ when $x \geq -3$ is $7 + \sqrt{x+3}$ .
The solution is $7 + \sqrt{x+3}$ .