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cupoosta [38]
3 years ago
12

Solve.

="TexFormula1" title=" \sqrt{3 x - 11} - \sqrt{x} + 5 = 6" alt=" \sqrt{3 x - 11} - \sqrt{x} + 5 = 6" align="absmiddle" class="latex-formula">

Mathematics
1 answer:
ICE Princess25 [194]3 years ago
5 0
Solve for x:
5 - sqrt(x) + sqrt(3 x - 11) = 6

Subtract 5 from both sides:
sqrt(3 x - 11) - sqrt(x) = 1

(sqrt(3 x - 11) - sqrt(x))^2 = -11 + 4 x - 2 sqrt(x) sqrt(3 x - 11) = -11 + 4 x - 2 sqrt(x (3 x - 11)) = 1:
-11 + 4 x - 2 sqrt(x (3 x - 11)) = 1

Subtract 4 x - 11 from both sides:
-2 sqrt(x (3 x - 11)) = 12 - 4 x

Raise both sides to the power of two:
4 x (3 x - 11) = (12 - 4 x)^2

Expand out terms of the left hand side:
12 x^2 - 44 x = (12 - 4 x)^2

Expand out terms of the right hand side:
12 x^2 - 44 x = 16 x^2 - 96 x + 144

Subtract 16 x^2 - 96 x + 144 from both sides:
-4 x^2 + 52 x - 144 = 0

The left hand side factors into a product with three terms:
-4 (x - 9) (x - 4) = 0

Divide both sides by -4:
(x - 9) (x - 4) = 0

Split into two equations:
x - 9 = 0 or x - 4 = 0

Add 9 to both sides:
x = 9 or x - 4 = 0

Add 4 to both sides:
x = 9 or x = 4

5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(4) + sqrt(3×4 - 11) = 4:
So this solution is incorrect

5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(9) + sqrt(3×9 - 11) = 6:
So this solution is correct

The solution is:
Answer:  x = 9
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Let x = state b , then x + 2 = state a

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4 0
3 years ago
3² • 9³ = [ ]<br>solve ​
RideAnS [48]

Answer:

3⁸ or 6561

Step-by-step explanation:

First, let's look at PEMDAS - Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

There are no parentheses, so let's solve the exponents.

3² • 9³

3² = 9

9³ = 729

Your expression is:

9 • 729

Now let's multiply.

= 6561

This number can also be expressed with exponents.

Since 9 = 3², 9³ = 3²⁽³⁾

Now your expression is:

3² • 3²⁽³⁾

First, solve the exponents by multiplying.

3² • 3⁶

When you multiply two expressions with exponents that have the same base (3), you add the exponents.

3² • 3⁶ = 3⁽²⁺⁶⁾ = 3⁸

3⁸ also equals  6561.

Your answer is 3⁸ or 6561.

Hope this helps!

4 0
3 years ago
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