Q. 144.4( 5 Votes )

The sum of two nu

Answer :

Given: a + b = 15



To find: The value of a and b.


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:


Numbers are ‘a’ and ‘b’


According to given conditions:


a + b = 15


b = 15 – a …. (1)


Also,


From (1),





15 × 10 = 3(15a – a2)


15 × 10 = 45a – 3a2


3a2 – 45a + 150 = 0


a2 – 15a + 50 = 0


a2 – 15a – 5a + 50 = 0


a (a – 10) – 5(a – 10) = 0


(a – 5) (a – 10) = 0


a = 5, 10


If a = 5, b = 15 – 5 = 10


If a = 10, b = 15 – 10 = 5


Hence, Numbers are 5,10 or 10, 5.


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