Question

the question is attached, please solve it.​

Answer 1

Solution

Given :-

• a^x = bc, b^y = ca , c^z = ab

Prove That :-

• x/(x+1) + y/(y+1) + z/(z+1) = 2

Explantion

Given in question

==> a^x = bc __________(1)

and,

==> b^y = ca ___________(2)

And,

==> c^z = ab __________(3)

Multiply equ(1) , equ(2) & (3)

we get,

==> a^x . b^y . c^z = (ab) . (bc). (ca)

==> a^x . b^y . c^z = a² . b² . c²

We Know,

If, p^m = p^n , then m = n .

So, using this identify .

First we take , a^x & a²

we get,

==> x = 2.

Now, take b^y & b²

==> y = 2

Now, take c^z & c²

==> z = 2

We want to Show here ,

• x/(x+1) + y/(y+1) + z/(z+1) = 2

Now, Take L.H.S.

= x/(x+1) + y/(y+1) + z/(z+1

keep value of x ,y & z

= 2/(2+1) + 2/(2+1) + 2/(2+1)

= 2/3 + 2/3 + 2/3

Take L.C.M. of denominator part

L.C.M. of 3 , 3, & 3 will be 3 .

we get,

= ( 2 + 2 + 2)/3

= 6/3

= 2

= R.H.S.

That's Proved.

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