Question

plz answer it best answer will be the brainliest answer.




if a and b are 2 positive integers such that a+b=ab+ba.then find the value of a^2+b^2

Answer 1

Two positive integers a and b are such that a + b =a/b + b/a. What is the value of a^2 + b^2?

S

a+b=a/b+b/aa+b=a/b+b/a

-> Now take L.C.M

a+b=(a2+b2)/aba+b=(a2+b2)/ab

-> Cross multiplying

(a+b)ab=a2+b2(a+b)ab=a2+b2

a2.b+b2.a=a2+b2a2.b+b2.a=a2+b2

Take a2a2 and b2b2 common

a2(b−1)+b2(a−1)=0a2(b−1)+b2(a−1)=0 --(1)

Now since aa and bb are positive integers - their square can’t be zero.

So in order to make the equation 1 equal to zero:

(b−1)(b−1) and (a−1)(a−1)both has to be 00.

Therefore,

b−1=0b−1=0 =>b=1b=1

and,

a−1=0a−1=0 =>a=1a=1

Hence a=b=1