Algebra Problem: If x+y=11, x.y=18, what is the x^2+y^2?

[Bamon]

If x+y=11, x.y=18, what is the x^2+y^2?

 

[Deleted member 4993]

If x+y=11, x.y=18, what is the x^2+y^2?

Hint:

(a + b)^2 = a^2 + b^2 + 2*a*b

 

[JeffM]

If x+y=11, x.y=18, what is the x^2+y^2?

You probably were taught several ways to solve two linear equations in two unknowns. Here you have two equations in two unknowns, but only one of those equations is linear.

Subhotosh's very clever hint is sufficient to answer this problem quite quickly. A general solution to this kind of problem is to use the technique of substitution that you already learned with respect to systems of linear equations.

\(\displaystyle x + y = 11 \implies y = 11 - x.\)

Now what would be your next step?

I reiterate: Subhotosh's suggestion is quicker for this particular problem whereas my suggestion works for any problem involving two equations in two unknowns.