Baffling math problem.?

Question

3 reasonably intelligent math tutors cannot for the life of them get this one:

xy = 1

x + y = 3

x^2 + y^2 = ?

What is the sum of x squared and y squared? Do we need to know what the values of x and y are?

Answer 1

x^2+y^2=(x+y)^2-2xy
substituting
x^2+y^2=3^2-2(1)
=9-2
=7
x^2+y^2=7
my 10 pointsplease

Answer 2

You don't need to solve for x and y, which is counter-intuitive. That's why these problems are so great. They force you to break your habits and think outside the box. The goal is to find a value for x^2 and y^2. How can we do this? we are given xy and x+y. If we square x+y, we have our terms x^2 and y^2. But we also have a term we don't want: 2xy. Wait! We have the value of xy, so that isn't a problem!


(x+y)^2 = x^2 + 2xy + y^2 = (3)^2=9
2(xy)=2(1)=2

We substitute 2 for 2xy and we get:

2 +x^2+y^2 = 9
x^2 + y^2 = 7


There! We solved the problem not knowing what x and y were. It was fairly simple once you realized the procedure (not extraordinarily large calculations or difficult algebra). There are similar problems like this, when you see a question in this form it's unlikely they'll want you to pound your head on the desk. There's usually a trick.

Answer 3

To find x^2+y^2, use the square formula:

(x+y)^2 = x^2 + 2xy + y^2
3^2 = (x^2+y^2)+2*1
9 = (x^2+y^2) + 2
9 - 2 = (x^2+y^2)

Therefore, x^2 + y^2 = 7. We did not need to know what x and y are, although they are solutions of the quadratic equation s^2 - 3*s + 1 = 0.

Answer 4

1.xy=1
so,2xy=2 (multiplying both side by 2 yields)
2.(x+y)=3
so,(x+y)^2=9 (squaring both sides yields)
so,x^2 + 2xy + Y^2 = 9 (because 2xy = 2)
so,x^2 + y^2 + 2 = 9
solving the equation gives x^2 + y^2 =7
the answer is 7.

Answer 5

x^2 + y^2 = 7

Start with (x+y)(x+y) = x^2 + 2xy + y^2, substitute 3 for x+y and 1 for xy.
(3)(3) = x^2 + 2 + y^2
x^2 + y^2 = 7

Answer 6

If x + y = 3
x² + 2xy + y² = (x + y)² = 9
So x² + y² + 2 = 9
x² + y² = 7.
We don't need to know x and y to solve this problem!

Answer 7

i think the answer is going to be 3y + 3x ... bc if u take the first equation (xy+1) and solve for X ... u get X=1/Y.

then, substitute this X value into the other equation and get 1/Y + Y = 3

(since 1/Y = X u can substitute it in)

and if u solve for Y you get: 1/y + y = 3
which becomes: 3y = y^2.

then, you do the exact same thing for X and u'll get 3x = X^2

so if u add Y^2 and X^2 you get 3x + 3y

Answer 8

i don't be responsive to why you may upload the only to the ninety 8. you're able to subtract the a million from the ninety 8 to get ninety seven returned. The ninety 8 represents the finished volume she owes. you does no longer upload an volume she has to an volume she owes. You subtract.