Question

If, x/lm-n^2=y/mn-l^2=z/nl-m^2, let us show that lx+my+nz=0​

Answer 1

Given : x/(lm-n²) =y/(mn-l²)=z/(nl-m²)

To Find : show that lx+my+nz=0​

Solution:

x/(lm-n²) =y/(mn-l²)=z/(nl-m²) = k

=> x = k(lm-n²)   = klm - kn²    

   y =  k(mn - l²) = kmn - kl²

   z  = k((nl-m²)  = knl - km²

lx  = kl²m -  kn²l

my = km²n -  kl²m

nz  = kn²l  - km²n

lx + my + nz  =  kl²m -  kn²l  + km²n -  kl²m +  kn²l  - km²n

=   kl²m   -  kl²m -   kn²l  +  kn²l +  km²n - km²n

= 0  

Hence lx + my + nz  = 0

QED

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Answer 2

Step-by-step explanation:

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