Chinese ancient mathematician Zhao Shuang's Pythagorean histogram is a large square composed of four congruent right triangles and a small square in the middle The area of a square is 13, the area of a small square is 1, the longer right side of a right triangle is a, the shorter right side is B, what is the value of a ^ 4 + B ^ 3

Chinese ancient mathematician Zhao Shuang's Pythagorean histogram is a large square composed of four congruent right triangles and a small square in the middle The area of a square is 13, the area of a small square is 1, the longer right side of a right triangle is a, the shorter right side is B, what is the value of a ^ 4 + B ^ 3

It's very simple
From the question, we can see that the side length of a small square is 1. From the graph, we can see that A-B = 1, so a = B + 1 (1)
Because the area of a large square is 13,13-1 = 12, the area of four right triangles is 12, and the area of each right triangle is 3, so the formula of triangle area is derived
AB / 2 = 3, ab = 6 substitute formula (1) into the solution to get b = 2, a = 3
So a ^ 4 + B ^ 3 = 89