1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Yakvenalex [24]
4 years ago
14

1. x=1/(root3-root2). find rootx-(1/rootx) 2. if x=[root(a+2b)+root(a-2b)]/[root(a+2b)-root(a-2b]. show that bx^2-ax+b=0

Mathematics
2 answers:
timofeeve [1]4 years ago
6 0
1. x = 1/ ( \sqrt{3} -  \sqrt{2)} = \sqrt{3}+  \sqrt{2};
 ( \sqrt{x} -1/ \sqrt{x} )^{2} = x + 1/x - 2 = = 
Svetllana [295]4 years ago
6 0
<h2>Answer with explanation:</h2>

Ques 1)

x=\dfrac{1}{\sqrt{3}-\sqrt{2}}

Now we are asked to find the value of:

\sqrt{x}-\dfrac{1}{\sqrt{x}}

We know that:

(\sqrt{x}-\dfrac{1}{\sqrt{x}})^2=x+\dfrac{1}{x}-2

Also:

x=\dfrac{1}{\sqrt{3}-\sqrt{2}} could be written as:

x=\dfrac{1}{\sqrt{3}-\sqrt{2}}\times \dfrac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}}\\\\\\x=\dfrac{\sqrt{3}+\sqrt{2}}{(\sqrt{3})^2-(\sqrt{2})^2}

since, we know that:

(a+b)(a-b)=a^2-b^2

Hence,

x=\dfrac{\sqrt{3}+\sqrt{2}}{3-2}\\\\\\x=\sqrt{3}+\sqrt{2}

Also,

\dfrac{1}{x}=\sqrt{3}-\sqrt{2}

Hence, we get:

(\sqrt{x}-\dfrac{1}{\sqrt{x}})^2=\sqrt{3}+\sqrt{2}+\sqrt{3}-\sqrt{2}-2\\\\\\(\sqrt{x}-\dfrac{1}{\sqrt{x}})^2=2\sqrt{3}-2\\\\\\\sqrt{x}-\dfrac{1}{\sqrt{x}}=\sqrt{2\sqrt{3}-2}

Hence,

       \sqrt{x}-\dfrac{1}{\sqrt{x}}=\sqrt{2\sqrt{3}-2}

Ques 2)

x=\dfrac{\sqrt{a+2b}+\sqrt{a-2b}}{\sqrt{a+2b}-\sqrt{a-2b}}

on multiplying and dividing by conjugate of denominator we get:

x=\dfrac{\sqrt{a+2b}+\sqrt{a-2b}}{\sqrt{a+2b}-\sqrt{a-2b}}\times \dfrac{\sqrt{a+2b}+\sqrt{a-2b}}{\sqrt{a+2b}+\sqrt{a-2b}}\\\\\\x=\dfrac{(\sqrt{a+2b}+\sqrt{a-2b})^2}{(\sqrt{a+2b})^2-(\sqrt{a-2b})^2}\\\\\\x=\dfrac{(\sqrt{a+2b})^2+(\sqrt{a-2b})^2+2\sqrt{a+2b}\sqrt{a-2b}}{a+2b-a+2b}\\\\\\x=\dfrac{a+2b+a-2b+2\sqrt{a+2b}\sqrt{a-2b}}{4b}\\\\\\x=\dfrac{2a+2\sqrt{a^2-4b^2}}{4b}\\\\\\x^2=(\dfrac{2a+2\sqrt{a^2-4b^2}}{4b})^2\\\\\\x^2=\dfrac{(2a+2\sqrt{a^2-4b^2})^2}{16b^2}

Hence, we have:

x^2=\dfrac{4a^2+4(a^2-4b^2)+8a\sqrt{a^2-4b^2}}{16b^2}\\\\\\x^2=\dfrac{4a^2+4a^2-16b^2+8a\sqrt{a^2-4b^2}}{16b^2}\\\\\\\\x^2=\dfrac{8a^2-16b^2+8a\sqrt{a^2-4b^2}}{16b^2}\\\\\\bx^2=\dfrac{8a^2-16b^2+8a\sqrt{a^2-4b^2}}{16b}\\\\\\bx^2=\dfrac{8a(a+\sqrt{a^2-4b^2})-16b^2}{16b}\\\\\\bx^2=\dfrac{8a(a+\sqrt{a^2-4b^2})}{16b}-\dfrac{16b^2}{16b}\\\\\\bx^2=\dfrac{a(a+\sqrt{a^2-4b^2})}{2b}-b\\\\\\bx^2=ax-b\\\\\\i.e.\\\\\\bx^2-ax+b=0

You might be interested in
The nature park has a pride of 7 adult lions and 4 cubs.
Levart [38]
The correct awnser is 54 i hope i help you
7 0
3 years ago
Read 2 more answers
Give an example of a number that is not real
goldfiish [28.3K]
5i because it is a imaginary number.
8 0
3 years ago
Read 2 more answers
7s^3-9s^2+s+6 need help
grigory [225]
(0,6)
enjoy have a great day.
7 0
4 years ago
What is the slope of function 3x-5y=17
Sliva [168]

Answer:

y=5/3x-3.4

Step-by-step explanation:

slope is 5/3

6 0
3 years ago
Read 2 more answers
Factor: a^2 m + 5am – 30m
DIA [1.3K]
I am gonna go with C.
6 0
3 years ago
Other questions:
  • Geometry question helpppppppp
    6·1 answer
  • Sherry was in charge of distributing 25 food items that were donated to the local food pantry. on Monday she distributed 8 items
    12·2 answers
  • Using the Unit Rate to Solve a Problem
    7·1 answer
  • Brett earns $19.20/h and he gets overtime for hours exceeding 40 per week. How many full hours must he work to earn a gross week
    13·2 answers
  • Photo included: Whats X+Y if...​
    11·2 answers
  • Question 1 (Fill-In-The-Blank Worth 4 points)
    11·1 answer
  • a designer created a scale drawing of a new kitchen. In the scale drawing, the length of the kitchen will be 8 feet. What scale
    10·1 answer
  • How do you graph y-1=3(x+6)
    13·2 answers
  • horn y ?????????????????????? ??????? ????????????bgfbxfdcfyctzfxc hcyxydyxhc h cyxtxf y ffsdvbnbf vgrgbxxcb hhfvsd am dj di​
    7·2 answers
  • Find the distance in feet of an object that travels 19,700 millimeters.<br> (1 meter ≈ 3.28 feet)
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!