Question

the difference of two positive number is 6 and their product is 216 find the number​

Answer 1

Answer:

The numbers are 18 and 12

Answer 2

Answer :-

Let the numbers be x and y.

According to the question :-

➩ $\rm x - y = 6$ - i

➩ $\rm xy = 216$ - ii

On squaring equation i

$\rm (x - y)^2 = 6^2$

$\rm x^2 + y^2 - 2xy = 36$

$\rm x^2 + y^2 - 2 ( 216 ) = 36$

$\rm x^2 + y^2 = 432 + 36$

➩ $\rm x^2 + y^2 = 468$ - iii

_____________________________

$\rm (x + y)^2 = x^2 + y^2 + 2xy$

$\rm (x + y)^2 = 468 + 2 ( 216 )$

$\rm (x + y)^2 = 468 + 432$

$\rm (x + y)^2 = 900$

$\rm x + y = \sqrt{900}$

➩ $\rm x + y = 30$ - iv

From equation i and iv -

➩ $\rm x - y = 6$

➩ $\rm x + y = 30$

By adding equation i and iv

$\rm x + x = 30 + 6$

$\rm 2x = 36$

➩ $\rm x = 18$

➩ $\rm y = 18 - 6 = 12$

Numbers = 18 and 12