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(3x+1)(2x+5)        you can finish

Find \(\frac{(a + b)^2 - 1}{ab} \)

Hello Guest!

\(a^3 + b^3 = a + b\\ a^3-a=b-b^3\)

\(\{a,b\}=\{-1,-1\},\{0,0\},\{1,1\}\)

\({\color{blue}\frac{(a + b)^2 - 1}{ab}}=\frac{(-1 + (-1))^2 - 1}{(-1)\cdot (-1)}\color{blue}=3 \\ {\color{blue}\frac{(a + b)^2 - 1}{ab}}=\frac{(1 + 1)^2 - 1}{1\cdot 1}\color{blue} =3\)

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find the value of x.

Hello Guest!

\((x+1/x):(x-7/x)=5:4\\ 4x+\frac{4}{x}=5x-\frac{35}{x}\\ \frac{35+4}{x}=x\\ x^2=39\)

\(x\in\{-\sqrt{39},+\sqrt{39}\}\\ x\in \{-6.245,6.245\}\)

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Cross multiply o get

(x+ 1/x)  * 4    =  (x- 7/x) * 5    then

4x  + 4/x   = 5x - 35/x             multiply through by x

4x^2 + 4 = 5x^2 - 35            simplify

x^2 - 39 = 0

x^2 = 39

x =  +- sqrt 39            sub in to see if true....check my math, but you should see the methodology to use

139  193  319  391  913  931  Total =  6 such numbers

Thanks you for sharing your thought.  This is what I want people to do.

Yes, there are reasons why this happens sometimes. 

Perhaps

1) The question does not make sense, intentionally or unintentionally.

2) The question is very advanced and no one knows how to answer it.

3) The question is very long, like a research question, which is not very suitable for this forum

3)  they have asked many questions in a row and it is obvious they are asking for their homeork to be done for them.

4) It is trivial and they can do it themselves.  Like on the site calculator or in their hads.

BUT

Their questions are far more likely to get a good answer than guest questions

AND

Both guests and memebers are encouraged to continue the thread. 

If they are not satisfied with the answer they should politely say so.

If they are happy they should say so too!

The radius of the circle is 8.

The largest integer k that works is 12.

The expected value is 3/7.

The answer is k = 5 + 2*sqrt(2).

There are 40 more students than before

40/ 200 X 100% = ............... % increase

(217800  -   2 * 5000) / 217800     *  100% = ...............%

cos C = 16/65

= 24

12y = 4x + 12

y = 4/12 x + 1

y = 1/3 x + 1

n ==12  and  14

2x - 5 <= x + 12

Subtract x from both sides to isolate x:

x - 5 <= 12

Add 5 to both sides:

x <= 17

In interval form: \([17, \infty)\)

Sometimes their questions don't get answered

10  20  30 ......90       9 times

(n-2)180  = sum of the progression  =  n/2 ( 120 + 120 + 5n - 5)

360n - 720 = 235n + 5 n^2

0 = 5 n^2 - 125 n + 720              

           Now use the quadratic formula to find   n = 9   or 16   ( 16 is too large for a convex polygon....the angle would be 200^o)

x = trainer 

y = bike = 40 - x

x * 8      +  ( 40 - x ) * 6 = 300          solve for 'x'      then   'y' = 40 -x

20 students less than 180

  20 / 180 * 100% = ............%

since when is the square root of 125 = 15?

Find the distance between the x-intercept and the y-intercept of the graph

Hello Guest!

\(3x-6y=18\\ y=\dfrac{x}{2}{ \color{blue}-3}=0\ ,\ \color{blue} x=6\)

\(P_1(0, \color{blue}-3)\\ P_2({ \color{blue}6},0)\)

\(D=\sqrt{6^2+(-3)^2}\)

\(D=6.7082\)

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