Post mathematic related questions here

[rst]

I think its just a condition
Also its looks true
example :-
f ³ (x) = 1 - x³ -3x
At x=1
f ³ (1) = 1 - (1)³ -3(1)

If f(1)= -1
-1 = 1-1 -3
-1 = -3
which is not true
So f(1) ≠ -1

 

[rst]

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NEW OBJECTIVE QUESTION

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[Niilesh]

Its too easy, ans is A) 34 (7*4+3*2)

 

[rst]

How did you get side 7 and 3 ??

 

[darkv0id]

^He must have got it via trial and error, I guess.

Only two whole numbers have the sum of their squares equal 58, i.e. 7 and 3.

 

[rst]

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Let side of small square be x
Let side of big square be y
Area of figure =58
x ² + y ² = 58
y=√ (58-x²)

It is defined for (58-x² ) ≥ 0
58 ≥ x²
√ 58 ≥ x
7.6 ≥ x

As x is whole number
x ∈ {0,1,2,..........,7}


As y is also whole number
So in y=√ (58-x²)
(58-x²) should give square number

Possible solutions are (3,7), (7,3)
As x<y
So only solution (3,7)
Side of small square=3
Side of big square =7
Perimeter = 7+7+7+3+3+3+4
=34 cm

 

[darkv0id]

^What's up with "2007" ?

 

[rst]

edited
Actually ,this question is similar to x ² + y ² = 2007 [page 7,post 185]
So I did copy and paste

 

[darkv0id]

edited
Actually ,this question is similar to x ² + y ² = 2007 [page 7,post 185]
So I did copy and paste

Ah ok.

 

[rst]

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[Niilesh]

How did you get side 7 and 3 ??

The Closest perfect sqaure no. less than 58 was 49 and 58 - 49= 9 = 3[sup]2[/sup]

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Ans is (4-3)*9 = 9

 

[rst]

Ans is (4-3)*9 = 9

Both ans and explanation are correct
well done !

 

[TheSloth]

@rst: Are you doing B.Tech?

 

[rst]

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[Niilesh]

If its single correct than ans will clearly be (D) . it can be proved with cosine law BTW.

Edit: Alternate method
first draw ab=6 then make a line at an angle of 30° from it at B. Now the least value of side AC will be the perpendicular distance of A from that line
AC≥6 Sin 30°
AC≥3

 

[rst]

If its single correct than ans will clearly be (D) . it can be proved with cosine law BTW.

Yeah
With cosine law ,we will get answer
cosB =(a² +c² -b² )/2ac

Edit: Alternate method
first draw ab=6 then make a line at an angle of 30° from it at B. Now the least value of side AC will be the perpendicular distance of A from that line
AC≥6 Sin 30°
AC≥3

It is also valid method

 

[Niilesh]

Then I think you misunderstood the question
f(x) is not part of f ³ (x)

The Question was right

*i.imgur.com/Tlmth3m.jpg
please explain your answer

We know that if a[sup]3[/sup] + b[sup]3[/sup] + c[sup]3[/sup] = 3abc then a + b + c = 0
Now,
f³(x) = 1 - x³ -3xf(x)
=> f³(x) + (-1)³ + x³ = -3xf(x)
=> f(x) -1 + x = 0
=> x= 1-f(x)

Now √(1- f(x)) is defined for 1- f(x) ≥ 0
=>x≥ 0
Domain --> R U {0}

 

[rst]

The Question was right



We know that if a[sup]3[/sup] + b[sup]3[/sup] + c[sup]3[/sup] = 3abc then a + b + c = 0
Now,
f³(x) = 1 - x³ -3xf(x)
=> f³(x) + (-1)³ + x³ = -3xf(x)
=> f(x) -1 + x = 0
=> x= 1-f(x)

Now √(1- f(x)) is defined for 1- f(x) ≥ 0
=>x≥ 0
Domain --> R U {0}

It is not necessary
for example
if a=1,b=1,c=1
then a[sup]3[/sup] + b[sup]3[/sup] + c[sup]3[/sup] = 3abc
but a + b + c = 3

 

[Niilesh]

^ Ohh you are right actually it is the reverse

 

[rst]

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