12
Step-by-step explanation:
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
We have,
Let the large number is =x
Square of smaller number is =8x
Now, According to given question,
x^2 −8x=180
⇒x^2 −8x−180=0
⇒x^2 −(18−10)x−180=0
⇒x^2−18x+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
