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Answer:

Let the numbers be x and y where x>y so,

x^2 - y^2 = 120.....(1)

y^2 = 2 x.....(2)

Putting (2) in (1), we get

x^2 - 2x = 120

x^2 - 2x - 120 = 0

x^2 - 12x + 10x - 120 = 0

x(x -12) +10(x - 12) = 0

(x-12)(x+10) = 0

So x can be 12 or -10, but we are given that the square of SMALLER number is twice the larger number, therefore the square of any number cant be negative,

Thus x cant TAKE value of -10

So x = 12, so y^2 = 2 (12)

y^2 = 24

So y = √24 or - √24

y = 2√6 or -2√6

Hence the numbers are 12 and 2√6 or 12 and -2√6

Step-by-step explanation:

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