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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