SOLUTION: 1...The sum of the two squares of two numbers is 4 and the difference of the squares of those two numbers is 1. Find the numbers 2...The sum of the square of the first number an

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Question 765924: 1...The sum of the two squares of two numbers is 4 and the difference of the squares of those two numbers is 1. Find the numbers
2...The sum of the square of the first number and the twice of the square of the second number is 6 and the twice of the first number take away the second number is 2. Find the two numbers.
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Answer by MaartenRU(13)   (Show Source): You can put this solution on YOUR website!
1.

Let's call the two numbers x and y. Then
and


Now we can see that, by subtracting the second equation from the first one, that

So

And
or
Substituting this into the first equation gives us

So

And therefore
or
2.

Same idea here. We're calling the two numbers x and y. We get


Now the problem is a bit trickier though. We can't really find the value of either x or y immediately, so we're going to use substitution.

According to the second equation,

We can rewrite this as

Now we substitute this 'implicit' value of y into our first equation:

We'll make that a bit nicer:

So,

Now, that's an equation we can solve. With the trusty old

We get

Dividing the numerator and denominator by two gives us

And so
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