(xm-xn) m+n (xn-xl) n+l (xl-xm) l+m = 1
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Answer:
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Step-by-step explanation:
(x
l
/x
m
)
1/lm
.(x
m
/x
n
)
1/mn
.(x
n
/x
l
)
1/nl
=( x^{l-m} ) ^{1/lm}. ( x^{m-n} ) ^{1/mn}. ( x^{n-l}) ^{1/nl}(x
l−m
)
1/lm
.(x
m−n
)
1/mn
.(x
n−l
)
1/nl
=x^{(l-m)/lm}. x^{(m-n)/mn}. x^{(n-l)/nl}x
(l−m)/lm
.x
(m−n)/mn
.x
(n−l)/nl
=x^{(l-m)/lm+(m-n)/mn+(n-l)/nl}x
(l−m)/lm+(m−n)/mn+(n−l)/nl
=x^{(ln-mn+lm-ln+mn-lm)/lmn}x
(ln−mn+lm−ln+mn−lm)/lmn
=x^{0}x
0
=1 (Proved)
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