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2014-09-15T11:54:29+05:30

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Let the positive number be x 
according to question 
√x + 12 = x 
⇒√x= x - 12
squaring both sides
⇒x= x² - 24x +144
⇒x² - 25x + 144 = 0 
⇒x² - 16x - 9x +144=0
⇒x(x - 16) - 9(x - 16)=0
⇒(x - 9)(x - 16)=0
so the number is 9,16

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2014-09-15T15:00:34+05:30

This Is a Certified Answer

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Consider the number is x
a/q,
          x = √x+12
⇒       12-x = -√x
on squaring both side of the equation ,    
 12^{2} -2.12.x+ x^{2} =(-  \sqrt{x}) ^{2}  \\  x^{2} -24x+144=x \\  x^{2} -24x-x+144=0 \\  x^{2} -25x+144=0 \\  x^{2} -16x-9x+144=0 \\ x(x-16)-9(x-16)=0 \\ (x-16)(x-9)=0
so,
                x-16 = 0 ⇒ x = 16
     and     x-9 = 0 ⇒ x= 9 
therefore numbers will be 9,16
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