If (x+y)^2=168 and xy =4, then x^2 + y^2=?
(x+y)^2 = 168
x^2 + 2xy + y^2 = 168
Replace xy with 4:
x^2 + 2*4 + y^2 = 168
x^2 + y^2 = 168 - 8 = 160.
Well, this problem looks like a puzzle where we have to find the value of x^2 + y^2. Let me try my hand at solving it while keeping things light-hearted!
So, first, let's expand (x+y)^2 = 168. That gives us x^2 + 2xy + y^2 = 168.
Since we know that xy = 4, we can substitute it back into the equation and simplify it a bit:
x^2 + 2(4) + y^2 = 168.
Now, we just need to find the value of x^2 + y^2.
Let's subtract 8 from both sides:
x^2 + y^2 = 168 - 8.
And voila! We have the solution. But, wait, before we reveal the final answer - let me entertain you a bit:
Why was the math textbook feeling sad?
Because it had too many problems!
Alright, back to the solution.
168 - 8 gives us 160. So, x^2 + y^2 = 160.
There you have it! x^2 + y^2 equals 160. I hope that puts a smile on your face, even if math doesn't always do the trick!
To solve the given equations, we can start by expanding the square of the sum of x and y.
(x+y)^2 = 168
Expanding this equation, we get:
x^2 + 2xy + y^2 = 168
We are also given that xy = 4. Substituting this value into the expanded equation, we have:
x^2 + 2(4) + y^2 = 168
Simplifying further:
x^2 + 8 + y^2 = 168
Now, to determine the value of x^2 + y^2, we need to isolate that term. We can do this by subtracting 8 from both sides:
x^2 + y^2 = 168 - 8
x^2 + y^2 = 160
Therefore, x^2 + y^2 is equal to 160.
To find the value of x^2 + y^2, we need to first expand the expression (x + y)^2.
(x + y)^2 can be written as (x + y)(x + y) using the formula for the square of a binomial.
Expanding this expression, we get:
(x + y)(x + y) = x(x + y) + y(x + y)
= x^2 + xy + yx + y^2
= x^2 + 2xy + y^2
We are given that (x + y)^2 = 168 and xy = 4. So, we can substitute these values into the expanded expression:
168 = x^2 + 2xy + y^2 (Substituting (x + y)^2 = 168)
168 = x^2 + 2(4) + y^2 (Substituting xy = 4)
168 = x^2 + 8 + y^2
Now, we need to isolate x^2 + y^2 on one side of the equation. Subtracting 8 from both sides:
168 - 8 = x^2 + y^2
160 = x^2 + y^2
Therefore, x^2 + y^2 = 160.