I did not understood how to solve

Asked by avishkargosavi89.9spicertl | 23rd Jun, 2020, 08:51: PM

Expert Answer:

It is given that x+y+z = 0
We need to find the value of (y+z)2/yz + (z+x)2/zx + (x+y)2/xy
 
fraction numerator open parentheses y plus z close parentheses squared over denominator y z end fraction plus fraction numerator left parenthesis z plus x right parenthesis squared over denominator z x end fraction plus fraction numerator open parentheses x plus y close parentheses squared over denominator x y end fraction equals fraction numerator open parentheses negative x close parentheses squared over denominator y z end fraction plus fraction numerator open parentheses negative y close parentheses squared over denominator z x end fraction plus fraction numerator open parentheses negative z close parentheses squared over denominator z y end fraction space space space space.... space U sin g space x plus y plus z equals 0
equals fraction numerator x squared over denominator y z end fraction plus fraction numerator y squared over denominator z x end fraction plus fraction numerator z squared over denominator z y end fraction equals fraction numerator x cubed over denominator x y z end fraction plus fraction numerator y cubed over denominator y z x end fraction plus fraction numerator z cubed over denominator x z y end fraction equals fraction numerator x cubed plus y cubed plus z cubed over denominator x y z end fraction
S i n c e space a cubed plus b cubed plus c cubed minus 3 a b c space equals space left parenthesis a plus b plus c right parenthesis left parenthesis a squared plus b squared plus c squared minus a b minus b c minus c a right parenthesis
W h e n space a plus b plus c equals 0 space rightwards double arrow a cubed plus b cubed plus c cubed minus 3 a b c space equals space 0 space rightwards double arrow space a cubed plus b cubed plus c cubed equals 3 a b c
rightwards double arrow fraction numerator x cubed plus y cubed plus z cubed over denominator x y z end fraction equals fraction numerator left parenthesis x plus y plus z right parenthesis left parenthesis x squared plus y squared plus z squared minus x y minus y z minus z x right parenthesis over denominator x y z end fraction equals fraction numerator 3 x y z over denominator x y z end fraction space space space.... space S i n c e space x plus y plus z equals 0
rightwards double arrow fraction numerator x cubed plus y cubed plus z cubed over denominator x y z end fraction equals 3
H e n c e comma space fraction numerator open parentheses y plus z close parentheses squared over denominator y z end fraction plus fraction numerator left parenthesis z plus x right parenthesis squared over denominator z x end fraction plus fraction numerator open parentheses x plus y close parentheses squared over denominator x y end fraction equals 3

Answered by Renu Varma | 24th Jun, 2020, 01:35: PM