Question

28. The difference of the squares of two positive integers is 180. The square of the smaller
number is 8 times the larger, find the numbers.​

Answer 1

Answer:let the two positive integers be x,y => given x²-y²=180 -------->[1] y²=8x--------->[2]

substitute [2] in [1]

=> x²-8x=180

=> x²-8x-180=0

=> x²-18x+10x-180=0

=> x(x-18)+10(x-18)=0

=> (x-18) (x+10) =0

=>x=18 (x is not equal to -10 since x is +ve integer)

from [2]y²=8x =8×(18) =144

:.y=+12,-12but y is also a +ve integer.

so, y= 12

:.two positive integers are 18,12