1.

find all natural triplets (a,b,c) with property a

Answer»

ANSWER:

The given equations are ab+bc=44 ..........(i)

And, ac+bc=23 .........(ii)

⇒c(a+b)=23, which is a prime number

So, the two factors must be 1 & 23.

c=1 and $$a + b = 23$$

⇒b=23−a

Put these values in (i), b(a+c)=44

⇒(23−a)(a+1)=44

⇒23a−a

2

+23−a=44

⇒a

2

−22a+21=0

⇒a

2

−21a−a+21=0

⇒a(a−21)−1(a−21)=0

⇒(a−21)(a−1)=0

⇒a=1,21

For, a=1,b=22

For a=21,b=2

∴b=22,2

The solution SETS are (1,22,1);(21,2,1).

Hence, the number of solutions sets =2.


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