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Ronit-Maths-problems


On Tue, Feb 9, 2010 at 3:18 PM, Ronit Sen wrote:

Dear Sir,
I am sending you some.Please try for it.

They are as follows:
1)Prove that for all real values of x, the expression 3x^2-6x+10 is always greater that 7.

2)If a^2+b^2+c^2=1 then prove that bc+ca+ab≥-1/2.

3)Find the equation to the straight line which passes through the point (-4,3)
and is such that the portion of the line between the axes is divided at the
point internally in the ratio 5:3.

I did the height and distance sum while giving you the sum.

Please send it to me as fast as possible..

Sir please send it fast.

Our Reply:
Hi Ronit,

Find the solutions as below:

1) we can write the expression as 3(x-1)^2+7, since (x-1)^2 will
always be positive, the minimum value of the expression will always be
7, even if x=1, ie, (x-1)^2 is zero.

So, your solution is:

3x^2-6x+10
=3(x-1)^2+7

Since a square is always positive, the minimum value of the exprssion
will always be 7.

2) (a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)

Now since (a+b+c) is a square, the value has to be greater than zero.

So, a^2+b^2+c^2+2(ab+bc+ca)>0,
So, 2(ab+bc+ca)>-(a^2+b^2+c^2)
So, ab+bc+ca>-1/2.

3) The formula to be used here is :

y2-y1/x2-x1=m/n
since it is dividing internally,

(y-3)/(x+4)=5/3

so the equation is: 5x-3y+29=0

Thanks

The Target ICSE team

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2 Responses to “Ronit-Maths-problems”

  1. sonam says:

    SIR PLEASE SEND ME THE SOLUTIONS OF THESE QUESTIONS….

    Q1. What is conversion in java ?

    Q2. Differentiate between :
    1) p = 6 & p = = 6
    2)SDA & DDA

    Q3) Answer the following :
    1)System.out.println(c=a+b); if a=5,b=6,c=10

    2)Debug: short z = (a + b)/2; if int a=6, b= 9;

    3)System.out.println(“CTC”+“supports”.substring(4));

    4)System.out.println(5 & 6);

    5)What is the difference between throw and throws?

    6)What are instance variable and instance methods

    7)math.rint(38.96)

    8) Design A Class amicable(int,int) with a default constructor, a parameterized constructor and the following two functions :

    1. checkAmicable(int,int) – this function returns true if the two arguments are amicable otherwise it returns false.
    2. main(int,int) – this function invokes the above function and prints whether the parameters passed to it are amicable or not.

    I SHALL BE GRATEFUL TO YOU…..

  2. john says:

    2)
    i) (p = 6)
    This means that the integral value of ‘6′ is assigned to the variable ‘p’.This is an assignment operator.
    (p == 6)
    These type of statements are used when we are checking a condition.Here we are checkinhg whether the value of the variable ‘p’ is ‘6′ or not.

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