Q. 74.2( 10 Votes )

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Answer :

Given: Let a, a+2 be two consecutive odd numbers.


a2 + (a + 2)2 = 394


To find: The value of a, a+2


Method Used:


To solve the quadratic equation by factorisation method, follow the steps:


1) Multiply the coefficient of x2 and constant term.


2) factorise the result obtained in step 1.


3) Now choose the pair of factors in such a way that after adding or subtracting(splitting) them


You get coefficient of x.


Explanation:


the consecutive odd integers be a, a + 2


According to question,


a2 + (a + 2)2 = 394


Split the middle terms.


a2 + a2 + 4a + 4 = 394


a2 + 2a – 195 = 0


a2 + 15a – 13a – 195 = 0


a (a + 15) – 13(a + 15) = 0


(a – 13) (a + 15) = 0


a = 13, -15


The numbers are 13 and 15.


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