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

Answer:

x^2-y^2=180

y^2=8x

x^2-8x-180=0

x^2-18x+10x-180=0

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

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

x=18;-10

Answer 2

Step-by-step explanation:

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 can't be negative)

x=18 is true (Positive value)

Now, square of small number

=18x=18×8=144

√144

=12

Hence, the answer is 12

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