Question

What should be the value of a.b.c if the we have positive integers of a, b and c such that the value of a square + b square=45 and b square+ c square =40.​

Answer 1

Answer:

for a+b+c=n, number of triplets a,b,c is given by, (n+1)(n+2)/2

This can be derived as follows,

consider (x+y+z)

n

for all the terms in the equation, sum of powers=n

therefore the number triplets such that a+b+c=n is equal to the number of terms in (x+y+z)

n

number of terms in (x+y+z)

n

is

2

(n+1)(n+2)

a+b+c<=8, a,b,c >0 minimum value of a,b,c=1. so replace a by a+1,b by b+!, c by c+1

Then, a+b+c<=5

a+b+c≤5=∑

r=0

5

n(a+b+c=r)

Solving the above equation, we get number of triplets=56

Step-by-step explanation:

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