Math Is Fun Forum

Dharshi

Member

Registered: 2006-10-31

Posts: 56

Help me

If a number x is twice as large as a number y and if the sum of their squares is 3125, then x and y are, respectively.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Help me

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Help me

In problems such as this, always write out x in terms of y (or vice-versa).  Then write an equation involving x and y, in this case the sum of squares equation.  Make a substitution and solve.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help me

Hi Dharsi;

  There is another way to get the answer that is useful. Especially if you only need the answer and the pressure is on to get it. It is guessing using binary splitting. It's given this name because each iteration halves the interval in which the answer must lie. It is common in numerical analysis and computer science. It works like this.

Choose some number for x

x=80
y=40
x^2+y^2=8000 too large. so split x.

x=40
y=20
x^2+y^2=2000: too small . 3125 is between x=40 and x=80 so split the difference between them.

x=60
y=30
x^2+y^2=4500: too large 3125 is between x=40 and x=60 so split the difference between them.

x=50
y=25
x^2+y^2=3125 Correct!

This is not a fluke, no starting pick of x<100 will take more than 7 guesses and this can done in your head.

Last edited by bobbym (2009-06-20 01:24:54)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Dharshi

Member

Registered: 2006-10-31

Posts: 56

Re: Help me

Thanks i got it

kant

Member

Registered: 2009-06-20

Posts: 1

Re: Help me

If a number x is twice as large as a number y and if the sum of their squares is 3125, then x and y are, respectively.

x = 2y
x²+y²= 3125

so (2y)² + y² = 3125

i.e: 4y² +y²  = 3125

         5y²   =  3125

          y²    =   3125 ÷ 5

                 =   625

          y     =   √625
                 =   25

  but  x = 2y

   so,    x = 2×25

              = 50

Answer:  x = 50
              y = 25 

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Help me

Multiplying x and y by -1 gets another solution, if you're interested in non-positives.

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Why did the vector cross the road?
It wanted to be normal.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,406

Re: Help me

Absolutely brilliant thinking, mathsy!

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.