Question

the difference of squares of two numbers is 180 the square of the smaller number is 8 times the larger number find the two numbers​

Answer 1

Step-by-step explanation:

x² - y² = 180 ---(1)

y² = 8x -----(2)

from equation (1) & (2)

x² - 8x - 180 = 0

x² - 18x + 10x - I80 = 0

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

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

x = 18✓

from eq.(2)

y² = 144

y = 12

The smaller number is 12 and the larger number is 18.

Answer 2

${\huge{\purple{\underline{\underline{Answer:}}}}}$

Let the smaller Number be = y

Let the larger Number be = x

According to the problem

The difference of squares of two numbers is 180

x² - y 1 = 180 -------------(1)

The square of the smaller number is 8 times.

y ² = 8x -------------(2)

y = √8x ------------(3)

Substitute equation (2) in equation (1)

We have :

x² - 8x = 180

x² - 8x - 180 = 0

x² - 18x + 10x - 180 = 0

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

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

if x - 18 = 0 and x + 10 = 0

So x = 18 and x = -10 ( minus neglected )

x = 18

y = √8x [ from equation (3)]

y = √8 × 18 = √144

y = 12

$\huge\mathfrak\pink{Sothelongerside = 18}$

$\huge\mathfrak\pink{Sothesmallerside = 12}$