Question

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

Answer 1

Answer:

18,12

Step-by-step explanation:

let a,b be the two no.s

given, a²-b² = 180 ------------- I

      & b² = 8a -------------------- II

substitute II in I, we get,

a² - 8a = 180

a² - 8a- 180=0

on factorising,

(a+10)(a−18) = 0

=> either a+10 =0 => a= -10 (Eliminate the negative no. as square of no.                               cannot be negative. see II )

   or        a-18 = 0 => a = 18

by II , b²=8*18

      => b² = 12²

    => b=12

Answer 2

Answer:

We have,

Let the large number is =x

Square of smaller number is =8x

Now, According to given question,

x2−8x=180

⇒x2−8x−180=0

⇒x2−(18−10)x−180=0

⇒x2−18x+10x−180=0

⇒x(x−18)+10(x−18)=0

⇒(x−18)(x+10)=0

⇒x−18=0,x+10=0

⇒x=18,x=−10

⇒x=−10,18

Either

x=−10 and x=18

x=18 is true (Positive value)

Now, square of small number

=18x=18×8=144

144

=12