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प्रश्न
If `"a"/("b + c") = "b"/("c + a") = "c"/("a + b")` , then prove that a(b - c) + b(c-a) + c (a - b) = 0
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उत्तर
`"a"/("b + c") = "b"/("c + a") = "c"/("a + b") = "k"`
a = k(b + c)
b = k(c+a)
c= k(a+b)
a (b - c)+ b (c - a)+ c (a - b) = 0
LHS
a (b - c)+ b (c - a)+ c (a - b)
= k (b + c )(b - c) + k ( c + a)( c - a) + k (a + b )(a - b)
= k(b2 - C2) + k( c2 - a2) + k( a2 - b2)
= kb2 - kc2 + kc2 - ka2 + ka2 - kb2
= 0 = RHS
LHS = RHS. Hence, proved.
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