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Question

5+252=m+n2

Find the value of m and n


A

We define for any positive integer 'n' and all positive real values of 'a'

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B

m=3 and n=2

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C

m=9 and n=103

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D

m=27and n=10

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Solution

The correct option is C

m=9 and n=103


Given that

5+252=m+n2
R.F of the denominator = 5 + 2

Multiplying both numerator and denominator by Rationalizing factor, we get

5+252 × 5+25+2 = m+n2

(5+2)2(5)2(2))2 = m+n2 [( a2b2=(a+b)(ab))]


25+102+23 = m+n2 [(a+b)2=a2+2ab+b2]

27+1023 = m+n2

273+1023 = m+n2

Comparing the coefficient , we have

m=9 and n=103


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