Question

The difference of square of two no.is45and square of smaller no.isfour times the larger no. Find two numbers

Answer 1

Answer:

the two numbers are 9 and 6

Step-by-step explanation:

Let two no/s be x(greater) and y(smaller)

Then acc to ques,

  x² - y² = 45          ...(1)

Also,  

        y² = 4x          ...(2)

From 1 and 2

Substituting 2 in 1

We get,  

    x² - y² = 45

    x² - 4x = 45

⇒ x² - 4x - 45

⇒ x² - 9x + 5x  -45

⇒ x(x - 9) + 5(x - 9)

⇒ (x+5)(x-9)

⇒ Then x = -5,9

If x = -5

  y² = 4(-5)

  y² = -20

  y  =  √-20       which is not applicable here

Negative neglected  

If x = 9

  y² = 4(9)

  y² = 36

   y = √36

   y = 6

Hence the no/s are 9 and 6

:)(: Hope This Helps !!! :)(:

Answer 2

Step-by-step explanation:

Let the two numbers be x and y such that y < x.

From the given conditions, we have:

x2 - y2 = 45 … (1)

y2 = 4x … (2)

Using (2) in (1), we have:

x2 - 4x - 45 = 0

(x - 9)(x + 5) = 0

x = 9 (Rejecting the negative value of x)

From (2), we get, y = 6 or -6

Rejecting the negative value, we have, y = 6.

Thus, the two numbers are 9 and 6.