# If a positive number exceeds its positive square roots by 12,then find the number.

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According to the question,

x - √x =12

⇒ x - 12 = √x

⇒ (x-12)² = (√x)²

⇒ x²+144-24x = x

⇒ x² -25 x+144=0

⇒ x² -16 x-9x+144=0

⇒ x(x-16)-9(x-16) = 0

⇒ (x-16)(x-9) = 0

⇒ x = 16 or 9

when x = 16, √x = 4; x-√x = 12 (satisfied)

when x = 9, √x = 3; x-√x = 6 (not satisfied)

So the number is 16.

Its square root be √x

x - √x = 12

x - 12 = √x

squaring on both sides

x²-24x+144 = x

x² - 25x + 144 = 0

(x-16)(x-9) = 0

x = 16 or 9