Question

the difference of square of two no.of is 180. the square of smaller no is 8 times the larger no. find the two number​

Answer 1

Step-by-step explanation:

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

therefore

x= 18 (since square of any number can't be negative)

Now, square of small number

⇒8x=18×8= 144

⇒144^1/2

⇒12

Answer 2

Answer:

Let the numbers be x and y

It is given x^2-y^2=180

y^2=8x

Substitute this value of y^2 in equation x^2-y^2=180

x^2-8x-180=0

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

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

This gives

x=18 and x=-10

Putting x=18 in equation y^2=8x we get

y^2=8×18 gives

y=12

x=-10 is not possible because that will give u=an imaginary number

So answer is x=18 and y=12