Certainly, let's solve this step by step:

Given:

1. [x - y] = 10

2. 2y = 23

First, let's solve for y using the second equation:

Divide both sides of the equation by 2:

y = 23 / 2

y = 11.5

Now, we know the value of y, let's substitute it into the first equation:

[x - y] = 10

[x - 11.5] = 10

Now solve for x:

Add 11.5 to both sides of the equation:

x - 11.5 + 11.5 = 10 + 11.5

x = 21.5

Now that we have the values of x and y:

x = 21.5

y = 11.5

We want to find x^2 + y^2:

x^2 = (21.5)^2 = 462.25

y^2 = (11.5)^2 = 132.25

Now add these values together:

x^2 + y^2 = 462.25 + 132.25 = 594.5

So, the value of x^2 + y^2 is 594.5.

Verified answer

x²+y²=?

(x-y) = 10

2xy = 23

(x-y)² = 10²

x²+y²-2xy = 100

x²+y² = 100+23 = 123