Question

the sum of two number is 37 and the difference of their squres is 185, thenthe difference of two number

Answer 1

x + y= 37 so y=37-x ⇒A
since x² - y²= 185 ⇒B 
putting the value of y in (B)
x² - ( 37-x)² = 185
x² - (1369 -74x +x²) = 185
x² -1369 + 74x -x²=185
74x= 185 + 1369
74x = 1574
x = 1574/74
x=21 then y= 16
And Difference between them is 5.

Hope It'll Help!!!!!!!!!!!

Answer 2

Answer:

let the numbers be x and y,

according to question,

x+ y = 37 .......i

and x² - y² = 185 ........ii

on dividing both equation,

$\frac{ { {x}^{2} - {y}^{2} } }{ x + y} = \frac{185}{37} \\ = > \frac{(x + y)(x - y)}{(x + y)} = 5 \\ = > x - y = 5$

,

x - y = 5 ........iii

wo, the difference between the two numbers is 5

Step-by-step explanation:

on solving equation i and iii we get

x = 21

and y = 16

so the numbers are 21 and 16..