Question

the difference of square of two numbers is 45 and the squareof a small number is 4 times of large number . find the numbers​

Answer 1

Answer:

9 and 6 or -5 and √-20

Step-by-step explanation:

Let the numbers be x and y.

x² - y² = 45   ...(i)

y² = 4x   ... (ii)

Using (ii) in (i)

x² - 4x = 45

x² - 4x - 45 = 0   ...(iii)

Factors of 45 are 1 , 45 ; 3 , 15 ; 5 , 9

5 - 9 = -4

(iii) can be written as

x² + 5x - 9x - 45 = 0

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

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

x - 9 = 0 or x + 5 = 0

x = 9 or x = -5

Using these values in (ii)

y² = 4 * 9 or 4 * -5

y² = 36 or -20

y = 6 or √-20

So the number are either 9 and 6 or -5 and √-20