# Q.1 If xyz=1, x + 1/z =5, y + 1/x =29, then find z + 1/y Q.2 If a+b+c=2, a^2 + b^2 + c^2 =6, a^3 + b^3 + c^3 =8, then find a^4 + b^4 + c^4.

Aman Bansal
592 Points
13 years ago

Dear Abhinav,

we can write x+(1/z) as (1/yz) + (1/z) solving this we get(1+y)/yz = 5 ................(1)

now from the second equation we get y + yz = 29

or, yz = 29-y putting it in (1) we get (1+y) = 5(29-y)

or, 1+y = 145 - 5y6y = 144or, y = 24now again putting it in (1) we get 25 = 120z

or, z = 5/24so x = 1/yz or, x = 1/5 notice that this fulfills the requirement xyz = 1so now z + 1/x =  z + zy = 5/24 + (5/24)(1/5) = 5/24 + 1/24 = 1/4 answer.

BEST OF LUCK..!!!!

Now you can win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

AMAN BANSAL

Rishabh Raj
29 Points
12 years ago

xyz=1, thus yz=1/x. x+1/z=5 so z=1/[5-x ] y+1/x=29 so y=[ 29x-1 ]/x Now, yz=1/x [ [29x-1 ]/x]*[1/[5-x ]] =1/x On solving, x=1/5 yz=5, y=24 z+1/y=[yz+1]/y. Substitute the values of yz and y. The answer u wud get as 1/4.