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
ANEK [815]
3 years ago
13

If x=2+√5 find the value of x²-1/x²

Mathematics
2 answers:
e-lub [12.9K]3 years ago
7 0

Answer:

8\sqrt{5}

Step-by-step explanation:

x = 2 + \sqrt{5}\\\\ x^{2} = (2+ \sqrt{5})^{2} \\\\ \ \ \ \ = 2^{2}+2* \sqrt{5}*2+( \sqrt{5})^{2}\\\\

 = 4 + 4 \sqrt{5}+5\\\\= 9+4 \sqrt{5}

\frac{1}{x^{2}}=\frac{1}{9+4\sqrt{5}}\\\\=\frac{1*(9-4\sqrt{5}}{(9+4\sqrt{5})(9-4\sqrt{5})}\\\\=\frac{9-4\sqrt{5}}{9^{2}-(4\sqrt{5})^{2}}\\\\=\frac{9-4\sqrt{5}}{81-4^{2}(\sqrt{5})^{2}}\\\\=\frac{9-4\sqrt{5}}{81-16*5}\\\\=\frac{9-4\sqrt{5}}{81-80}\\\\=\frac{9-4\sqrt{5}}{1}\\\\=9-4\sqrt{5}

x^{2}-\frac{1}{x^{2}}= 9 + 4\sqrt{5} -(9 - 4\sqrt{5})\\\\

            = 9 + 4\sqrt{5} - 9 + 4\sqrt{5}\\\\= 9 - 9 + 4\sqrt{5} + 4\sqrt{5}\\\\= 8\sqrt{5}

natta225 [31]3 years ago
3 0

Answer:

{ \tt{ {x}^{2}  -  \frac{1}{ {x}^{2} } }} \\  = { \tt{ {(2 +  \sqrt{5} )}^{2} -  \frac{1}{ {(2 +  \sqrt{5}) }^{2} }  }} \\  = { \tt{ \frac{(2 +  \sqrt{5} ) {}^{4}  - 1}{ {(2 +  \sqrt{5} )}^{2}  } }} \\  = { \tt{ \frac{(9 + 4 \sqrt{5}) {}^{2}  }{ {(9 +  4\sqrt{5}) }}}} \\  = { \tt{9 + 4 \sqrt{5} }}

You might be interested in
Which angle must have the same measure as angle x
Savatey [412]

Answer:

Two angles that have the same measure are called congruent angles. Here are two angles that both measure 30°. We say that angle x is congruent to angle y.

Step-by-step explanation:

4 0
3 years ago
Bought to video games for a total of $55 their prices have a difference of $15
shepuryov [24]

Answer:

The answer is 40

Step-by-step explanation:

55-15=40

5 0
3 years ago
Which one of the following statements is true?
Katarina [22]

Answer:

A

Step-by-step explanation:

Because the gravity of the earth

3 0
3 years ago
Read 2 more answers
Can you help me with all 15 questions on the test ​
Schach [20]

Answer:

i can try just put the questions up

Step-by-step explanation:

7 0
3 years ago
A salesperson makes 18% commission on every TV sold. If the salesperson sold four TV’s at $885 each, how much commission did the
Levart [38]

Answer:

They made a $531 commission.

Step-by-step explanation:

The given is:

  • The price of each TV is $885
  • The commission is 18% on every TV sold
  • The salesperson sold 4 TV's

We need the value of the commission

Let us find the commission of every TV, then find the total amount of all

∵ The price of each TV is $885

∵ The commission is 18 %

→ Find 18% of $885

∴ The commission on every TV = 885 × 15%

∴ The commission on every TV = 885 × 15/100

∴ The commission on every TV = $132.75

∵ The salesperson sold 4 TV

∴ The commission on them = 4 × 132.75

∴ The commission on them = $531

They made a $531 commission.

5 0
3 years ago
Other questions:
  • QUICKKKKKKKK<br> EXPERTS/ACE/TRUSTED HELPERS
    8·1 answer
  • Suppose the null hypothesis, H0, is: a sporting goods store claims that at least 70% of its customers do not shop at any other s
    14·1 answer
  • First 20 minutes ,they traveled 15 miles ,at the same rate how fat will they have traveled in 2 and a half hours .Enter as integ
    14·1 answer
  • Help!? Helping my son with geometry ... I have no clue what I’m doing here
    12·1 answer
  • Help me please someone i’m stressing out rn :(
    15·1 answer
  • Can someone please help me answer this question asap thank
    7·1 answer
  • The summit of a volcano is 10 kilometers above ocean floor.
    13·1 answer
  • To make sure there is enough space for the donuts, Dave wants to add 2 inch to the minimum length, width, and height of the box.
    10·2 answers
  •  In a survey of 1,800 people who owned a certain type of​ car, 990 said they would buy that type of car again. What percent of t
    7·1 answer
  • Can someone help me answer some of these questions?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!