Let x = √(4-√7) and y = √(4+√7), then value of (x-y/√3)² + (x²y+xy²)²+(x+y)² is -
Answers
Given info:- X = √(4-√7) and Y = √(4+√7)
Find the value of [(X-Y)/√3]²+(X²Y+XY²)²+(X+Y)²?
Explanation:-
Given that:
X = √(4-√7)
It can be written as
On multiplying and dividing by 2 in the squre root
⇛ X = √[2{(4-√7)}/2]
⇛ X =√[(8-2√7)/2]
⇛ X =√[{(7+1)-2√7{/2]
⇛ X =√[{(√7)²+(√1)²-2(√7)(√1)}/2]
It is in the form of a²-2ab+b²
Where , a = √7 and b = √1
⇛X = √[{(√7-√1)}²/2] [∵(a-b)² = a²-2ab+b²]
⇛ X = (√7-√1)/√2
⇛ X = (√7-1)/√2 — — — — Eqⁿ(1)
and
Y = √(4+√7)
It can be written as
On multiplying and dividing by 2 in the squre root
⇛ Y = √[{2(4+√7)}/2]
⇛ Y =√[(8+2√7)/2]
⇛ Y =√[{(7+1)+2√7}/2]
⇛ Y =√[{(√7)²+(√1)²+2(√7)(√1)}/2]
It is in the form of a²+2ab+b²
Where , a = √7 and b = √1
⇛Y = √[{(√7+√1)}²/2] [∵(a+b)² = a²+2ab+b²]
⇛ Y = (√7+√1)/√2
⇛ Y = (√7+1 )/√2 — — — — Eqⁿ(2)
On adding Eqⁿ (1) & Eqⁿ(2)
→ X+Y = (√7-1)/√2+(√7+1)/√2
→ X+Y = (√7-1+√7+1)/√2
→ X+Y = (2√7 )/√2
→ X+Y = (√2×√2×√7)/√2
→ X+Y = √2×√7
→ X+Y = √14 — — — — Eqⁿ(3)
On Subtracting Eqⁿ(2) from Eqⁿ(1)
→ X-Y =[(√7-1)/√2]-[(√7+1)/√2]
→ X-Y =[ (√7-1 )-(√7+1)]/√2
→ X-Y = (√7-1-√7-1)/√2
→ X-Y = (-1-1)/√2
→ X-Y = -2/√2
→ X-Y = -(√2×√2)/√2
→ X-Y = -√2 — — — — Eqⁿ(4)
On multiplying Eqⁿ(1)& Eqⁿ(2)
→ XY = [(√7-1)/√2][(√7+1)/√2]
→ XY = (√7-1)×(√7+1)/(√2×√2)
→ XY = [(√7)²-(1)²]/(2) [∵(a+b)(a-b) = a²-b²]
→ XY = (7-1)/2
→ XY = 6/2
→ XY = 3 — — — — — Eqⁿ(5)
Now,
The value of [(X-Y)/√3]²+(X²Y+XY²)²+(X+Y)²
It can be written as
⇛[(X-Y)²/3] + [ XY(X+Y) ]²+(X+Y)²
From Eqⁿ(3), Eqⁿ(4)& Eqⁿ(5)
⇛ [(-√2)²/3] + [ 3(√14)]²+(√14)²
⇛ (2/3) + (9×14)+(14)
⇛ (2/3)+(126)+(14)
⇛ (2/3)+140
⇛ [2+(3×140)]/3
⇛(2+420)/3
⇛ 422/3
Therefore, the value of [(X-Y)/√3]²+(X²Y+XY²)²+(X+Y)² is 422/3.
If you have any doubt, then you can ask me in the comments.
Related Questions
the sum of 2 numbers is 99 and their quotient is 8What are the 2 numbers
Answers
Answer:
11 and 88
Step-by-step explanation:
I just set up a system of equations:
x + y = 99,
x/y = 8
I decided to use the method of substitution which is expressing one variable in terms of the other and substituting it into the other equation.
To use substitution, I changed the second equation to:
x = 8y
And then, I substituted that value for x into the first equation:
8y + y = 99
And that means:
9y = 99
Hence, y = 11. To find the second number, just substitute 11 for y in the first equation to get:
x + 11 = 99
And that means x = 88.
Savannah is deciding between two parking garages. Garage A charges an initial fee of $9 to park plus $1.50 per hour. Garage B charges an initial fee of $4 to park plus $2.50 per hour. Let A A represent the amount Garage A would charge if Savannah parks for t t hours, and let B B represent the amount Garage B would charge if Savannah parks for t t hours. Graph each function and determine which garage would be cheaper if Savannah needs to park for 6 hours.
Answers
Answer:
A = 10 + 3t
B = 3 + 4t
if t = 12 , then A = 10 + 3(12) = $46, B = 3 + 4(12) = $51.
So Garage A is cheaper for 12 hours
Step-by-step explanation:
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Answers
Answer:
See below:
Step-by-step explanation:
So we want to know what 9 to the -8th exponent will be if I understand your question right.
To solve for [tex]9^{-8}[/tex] we first have to solve for [tex]9^{8}[/tex] which would be 43046721.
Now, if we have a negative number, the answer would be 1 divided by that number, so therefore, we get [tex]9^{-8} =\frac{1}{43046721}[/tex]
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Answer:
1) A) 64 tickets
B) $11
2) A) 20 rides
Step-by-step explanation:
1) a) set y to 37 because they made 37 dollars
37 = 0.50x + 5
32 = 0.50x.........subtract 5 from both sides
64 = x..................divide both sides by 0.50 to get x by itself
b) set x to 12 because x is the amount of ride tickets they bought
y = 0.50(12)+ 5
y = 6 + 5............multiply 12 by 0.50
y=11......................add
2) a) set both equations equal to each other to see when they will be equal
0.50x + 5 = 0.75x
0.50x = 0.75x - 5..........subtract 5 from both sides
0.50x - 0.75x = - 5........subtract 0.75x from both sides
-0.25x = - 5......................combine like terms
x=20...................................divide both sides by -0.25 to isolate x
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
85% of 540 = 30% of C
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C = 1530
Answer:
c = 1530
Step-by-step explanation:
First, convert the percentages to a decimal.
[tex]85\div100=0.85\\30\div100=0.30[/tex]
In decimal form, percentages are a fraction of 1. 0 is 0%, 0.5 is 50%, and 1 is 100%.
With that, you can write this equation:
[tex]0.85\times540=0.3\times c[/tex]
Now, just solve for c:
[tex]0.3c=0.85\times540\\0.3c=459\\c=1530[/tex]
To confirm that:
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Answer:
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Answer:
listed below
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2
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Step-by-step explanation:
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