SOLUTION: Two farmers always plant their mango trees in square arrays.This year they planted 11 more mango trees in their square, how many mango trees are there in the garden this year?

Two farmers always plant thier mango trees in square arrays. This year they
planted 11 more mango trees in their square, how many mango trees are there in
the garden this year?

Let last year's number of trees be x²

Then this year's number of trees = y²

>>...This year they planted 11 more mango trees in their square...<<

So therefore

            y² = x² + 11

       y² - x² = 11

(y - x)(y + x) = 11

The only factors of 11 are 11 and 1,
so

the smaller factor, y - x, must = 1 and
the larger factor, y + x, must = 11

So we have this system of equations

y - x =  1
y + x = 11

Solving that system we get y = 6, x = 5

So this year there were y² or 6² or 36 mango trees.

That's the answer asked for.

[Last year there were x² or 5² or 25 mango trees.]

Edwin