Sign In Sign Up Ask an AI advisor

tonimgreen17p6vqjq

tonimgreen17p6vqjq

12.08.2020 •

Mathematics

If $\sqrt{5} x = \sqrt{3} x + \sqrt{7}$
find the value of x in the form

$\sqrt{ \frac{a}{b} }$

Solved

Show answers

Ответ:

chandataylor4215

31.01.2022

$x=\sqrt{\frac{7(4+\sqrt{15})}{2}}$

Step-by-step explanation:

From the way it is written, the is outside the square root. I will rewrite it as:

$x\sqrt{5} =x\sqrt{3} +\sqrt{7}$

$x\sqrt{5}-x\sqrt{3}=\sqrt{7}$

$x(\sqrt{5} - \sqrt{3} )=\sqrt{7}$

$x= \frac{\sqrt{7} }{\sqrt{5} - \sqrt{3}} \implies \frac{\sqrt{7}(\sqrt{5} + \sqrt{3}) }{2}$

$x=\frac{1}{2} \sqrt{7} (\sqrt{5} + \sqrt{3} )$

$x=\frac{\sqrt{35}}{2} +\frac{ \sqrt{21}}{2}$

$x=\frac{\sqrt{35}+\sqrt{21}}{2}$

Multiply denominator and numerator by 3

$x=\frac{3\sqrt{35}+3 \sqrt{21}}{6}$

Factor $\sqrt{3}$

$\sqrt{3} (\sqrt{105}+3 \sqrt{7})$

$x=\frac{\sqrt{3} (\sqrt{105}+3 \sqrt{7})}{6}$

Divide denominator and numerator by $\sqrt{3}$

$x=\frac{\sqrt{105}+3 \sqrt{7}}{2\sqrt{3} }$

Let's rewrite it again

$x=\frac{\sqrt{ (\sqrt{105}+3 \sqrt{7})^2}}{\sqrt{12} }$

$x=\sqrt{ \frac{1}{12} \cdot (\sqrt{105}+3 \sqrt{7})^2}$

It is already in the form $\sqrt{\frac{a}{b} }$

Expanding the perfect square, we have

$63+42\sqrt{15}+105$

$\frac{63}{12} +\frac{42\sqrt{15}}{12} +\frac{105}{12}$

$\frac{21}{4} +\frac{7\sqrt{15}}{2} +\frac{35}{4}$

Factor $\frac{7}{2}$

$\frac{7}{2} (4+\sqrt{15} )$

Therefore,

$x=\sqrt{\frac{7}{2} \left(4+\sqrt{15} \right)}$

$x=\sqrt{\frac{7(4+\sqrt{15})}{2}}$

0,0(0 оценок)

Ответ:

shavonfriend27

16.11.2022

The answer is A. 28/53

0,0(0 оценок)

Ask your question to the AI advisor

Ai-bot is an expert in any field and is the perfect companion for reliable and useful answers and advice on a variety of topics, including science, history, technology, art, sports, health, culture and more.

Ask your question

More tips

F Food and Cooking Discovering the Mysterious Fruit of Feijoa...
B Business and Finance How to Open an Online Store? A Detailed Guide for Beginners...
W Work and Career How to Write a Resume That Catches the Employer s Attention?...
C Computers and Internet Е-head: How it Simplifies Life for Users?...
F Family and Home How to Choose the Best Diapers for Your Baby?...
F Family and Home Parquet or laminate, which is better?...
L Leisure and Entertainment How to Properly Wind Fishing Line onto a Reel?...
L Leisure and Entertainment How to Make a Paper Boat in Simple Steps...
T Travel and tourism Maldives Adventures: What is the Best Season to Visit the Luxurious Beaches?...
H Health and Medicine Kinesiology: What is it and How Does it Work?...

Answers on questions: Mathematics

M Mathematics Help plz 8th grade math graphs I need helpppppp...
M Mathematics Are 12/102 and 18/153 equivalent ratios?...
M Mathematics 1) [5pts] Here is the scenario: Suppose that 8% of the apples picked from an orchard do not meet high quality standards to sell. When a truckload of apples arrives at a packing...
M Mathematics In AOPQ, the measure of angle Q=90°, the measure of angle O=66°, and QO = 4.5 feet. Find the length of OP to the nearest tenth of a fo...
M Mathematics Find the length of arc AD. Use 3.14 for . Round to the nearest tenth. 7.9 cm B 66.4 C [ ? ]cm Enter...
M Mathematics Entrance to a new arcade On a weekday cost $15 and tokens Our $.50 each if you go on a weekend the only charge $12 entrance fee but tokens or $.75 each T= the number of tokens...
M Mathematics When solving the system of equations below, what is the appropriate substitution? y = 10x + 1 y = 2x – 5 2x - 5 = 10x + 1 O y = 10(2x - 5) + 1 O y = 2(10x + 1)-5...
M Mathematics 4.(02.07) The figure shows two parallel lines AB and DE cut by the transversals AE and BD: А B 2 3 С 4 6 5 D E Which statement best explains the relationship between AABC and AEDC?...
M Mathematics How many feet are in half a mile?...
M Mathematics Solve for n. 5 (n+11) = 5 • 9 + 5 • 11...

S Sport S Society and Politics G Goods and services C Cities and Countries A Animals and plants L Legal consultation W Work and Career C Construction and repair H Health and Medicine D Dating, Love, Relationships H Horoscopes, Magic, Divination S Style and Beauty L Leisure and Entertainment S Science and Technology P Photography and Videography A Art and Culture O Other P Philosophy F Food and Cooking B Business and Finance T Travel and tourism F Family and Home A Auto and Moto

Show more

Full access

It will provide effective and fast learning by providing unlimited access to the knowledge base and receiving answers from experts and an AI advisor.

Subscribe

Ask an AI advisor a question

I want advice

ABOUT US

About us
Terms of use
Copyright
Privacy Policy
Cookie policy
Cookie preferences

HELP

Sign Up
FAQ
Security Center

App

Spanish Geography Health Engineering Arts Social Studies Advanced Placement (AP) German SAT History Computers and Technology Physics Chemistry Biology Law Mathematics World Languages French Business Medicine