Question

the difference of squares of rwo number is 45. the squares of the smaller number is 4 times the larger number.determine the number

Answer 1

x^2 - y^2 =45
y^2 =4x
x^2 -4x -45 =0
x^2 -9x+5x-45=0
x= 9, -5
-5 rejected
So x=9
So y^2 =4 ×9
Y= 2×3=6

Answer 2

Let  y < x
       x^2 – y^2  = 45   ,   y^2 = 4x
=>   x^2 – 4x = 45
=>   x^2 – 4x - 45 = 0
=>   (x – 9)(x + 5) = 0
=>  x = 9 , -5
=>  y2 = 4*9  ,  4*(-5)
           = 36 , -20 (rejected , since y^2 cannot be (-ve) )
y = 6

Therefore , the numbers are ‘9’ and ‘6’ .

Hope it helped .