two consectuive perfect squares differ by 59. what is the larger of these two perfect squares?

Answer 1

x^2 - y^2 = 59

x and y are integers

64-59=5

81-59 = 22

100-59 = 41

121-59 =62

169-59= 110

14^2 -59 = 196-59= 137

15^2 -59=225-59=166

16^2-59 = 256-59= 197

17^2 -59 = 289-59= 240

18^2 -59 = 324-59 = 265

19^2 -59 = 361-59= 302

20^2 -59 = 400-59= 341

21^2 -59= 441-59= 382

22^2 -59 = 484-59= 425

23^2 -59= 529-59 = 470

24^2-59= 576-59= 517

25^2 -59= 625-59= 566

26^2 -59= 676-59= 617

27^2 -59= 729-59 = 670

28^2 -59 = 784-59= 725

29^2 -59= 841-59 = 782

30^2-59 = 900-59 = 841

Bingo

30^2 -29^2 = 59. 30 and 29 are consecutive integers

the larger perfect square = 900