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A positive integer is of the form 3q+1.can you write its square in any other form than 3q+1 i.e.3m or 3m+2for some integer m?justify your answer

Posted by Rohan Singh 6 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Ram Kushwah 6 years, 7 months ago

No , square of any positive integer of the form 3m + 1 is always in the form in the 3m + 1 ,

but it'snot in the form of - Either 3m or 3m + 2 because of the following solution :

⇒ a = bq + r

Let ''a'' be any positive integer and 'q be the quotient and let ''r'' be the remainder .

Therefore we get ,

a² = ( 3 q + 1 )² { We square it , as according to the question }

a² = 9 q² + 6 q² + 1² { (a + b )² = a² + b² + 2 a b }

a² = 3 ( 3 q² + 2 q²) + 1

a² = 3 q + 1 ( Where , q is 3 q + 1 )

So, we got that a² is always in the form of 3 q + 1.

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CBSE > Class 10 > Mathematics