I know the answers, I just don't know how to solve it and show my work.
1. (3√6 + 5√10)^2 - 286 + 60√15
2. (2 + √10)(2 - √10) - -6
3. y = √6x-18 - x (greater then or equal to) 3
Thank you
I assume you want to simplify the first two
1. (3√6 + 5√10)^2 - 286 + 60√15
You must know how to square a binomial ...
= 54 + 30√60 + 250 - 286 + 60√15
= 18 + 60√15 + 60√15
= 18 + 120√15
2. the first part is the expansion of a difference of squares pattern, you must know that
3. y = √6x-18 - x
what about it?
Fail. It wrote it wrong. These are the problems:
(3√6 + 5√10)^2
y = √6x-18
I solved the second one.
Here are my answers, I just need to know how to solve:
286 + 60√15
x (greater than or equal to) 3
Of course, if you knew how to solve them, you would naturally know how to show your work ...
#1 As always, (a+b)^2 = a^2+2ab+b^2
(3?6 + 5?10)^2
= (3?6)^2 + 2(3?6)(5?10) + (5?10)^2
= 54 + 30?60 + 250
= 304 + 60?15
So,
(3?6 + 5?10)^2 - 286 + 60?15
= 304+60?15 - 286 + 60?15
= 18 + 120?15
#2 As always, (a+b)(a-b) = a^2-b^2
(2 + ?10)(2 - ?10) - -6
= 2^2 - (?10)^2 + 6
= 4 - 10 + 6
= 0
#3
y = ?(6x-18)
y = ?6 ?(x-3)
This is just the graph of y=?x
shifted right 3 and stretched vertically by a factor of ?6
http://www.wolframalpha.com/input/?i=%E2%88%9A(6x-18)
1.
( a + b ) ^ 2 = a ^ 2 + 2 a * b + b ^ 2
so
( 3 √6 + 5 √10 ) ^ 2 = ( 3 √6 ) ^ 2 + 2 * 3 √6 * 5 √10 + ( 5 √10 ) ^ 2
( 3 √6 + 5 √10 ) ^ 2 - 286 + 60 √15 =
( 3 √6 ) ^ 2 + 2 * 3 √6 * 5 √10 + ( 5 √10 ) ^ 2 - 286 + 60 √15 =
3 ^ 2 * 6 + 6 * √6 * 5 √10 + 5 ^ 2 * 10 - 286 + 60 √15 =
9 * 6 + 30 * √6 * √10 + 25 * 10 - 286 + 60 √15 =
54 + 30 * √ ( 6 * 10 ) + 250 - 286 + 60 √15 =
18 + 30 * √60 + 60 √15 =
18 + 30 * √( 4 * 15 ) + 60 √15 =
18 + 30 * √ 4 * √15 + 60 √15 =
18 + 30 * 2 * √15 + 60 √15 =
18 + 60 √15 + 60 √15 =
18 + 120 √15 =
6 * 3 + 6 * 20 √15 =
6 ( 3 + 20 √15 )
2.
( 2 + √10 ) ( 2 - √10 ) - -6 =
( 2 + √10 ) ( 2 - √10 ) + 6
( a + b ) ( a - b ) = a ^ 2 - b ^ 2
in this case:
( 2 + √10 ) ( 2 - √10 ) = 2 ^ 2 - ( √10 ) ^ 2 = 4 - 10 = - 6
So:
( 2 + √10 ) ( 2 - √10 ) - -6 =
( 2 + √10 ) ( 2 - √10 ) + 6 =
- 6 + 6 = 0
3.
y = √6x-18 - x (greater then or equal to) 3 doesn't make sense.
But:
√ 6 x -18 - x ≥ 3 Add 18 to both sides
√ 6 x -18 - x + 18 ≥ 3 + 18
√6 x - x ≥ 21
x ( √6 - 1 ) ≥ 21 Divide both sides by ( √6 - 1 )
x = 21 / ( √6 - 1 )
As you can see from the responses here, if you want a good answer, you need to be clear on just what it is you are asking.
It is not our job to figure out what you mean -- it is your job to say it so clearly that you cannot be misunderstood!
Sure! I'll help you go through each question and explain how to solve it step by step.
1. (3√6 + 5√10)^2 - 286 + 60√15:
To simplify this expression, we need to apply the distributive property and simplify each term:
First, let's square the binomial (3√6 + 5√10)^2:
(3√6 + 5√10)^2 = (3√6)^2 + 2(3√6)(5√10) + (5√10)^2
= 9*6 + 2*3√6*5√10 + 25*10
= 54 + 30√60 + 250
= 304 + 30√60
Next, we substitute this back into the original equation:
304 + 30√60 - 286 + 60√15
Now, we combine like terms:
304 - 286 + 30√60 + 60√15
Finally, we simplify the expression:
18 + 30√60 + 60√15
2. (2 + √10)(2 - √10) - (-6):
To simplify this expression, we can use the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b):
(2 + √10)(2 - √10) = 2^2 - (√10)^2
= 4 - 10
= -6
3. y = √6x - 18 - x (greater than or equal to) 3:
To solve this equation, we can follow these steps:
Step 1: Isolate the square root term:
Add x to both sides of the equation:
y + x = √6x - 18
Now, we have isolated the square root term on the right side.
Step 2: Square both sides of the equation:
(y + x)^2 = (√6x - 18)^2
Squaring both sides eliminates the square root.
Step 3: Simplify the equation:
(y + x)(y + x) = (√6x)^2 - 2(√6x)(18) + 18^2
y^2 + 2xy + x^2 = 6x - 2(18√6x) + 324
y^2 + 2xy + x^2 = 6x - 36√6x + 324
Step 4: Move all terms to one side to set the equation to zero:
y^2 + 2xy + x^2 - 6x + 36√6x - 324 = 0
This is the final equation that represents the given inequality. To find the solution, you may need to further simplify or graph it, depending on the requirements.