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प्रश्न
If `x/(b + c - a) = y/(c + a - b) = z/(a + b - c)` prove that each ratio’s equal to : `(x + y + z)/(a + b + c)`
उत्तर
`x/(b + c - a) = y/(c + a - b) = z/(a + b - c)` = k(say)
x = k(b + c – a),
y = k(c + a – b),
z = k(a + b – c)
`(x + y + z)/(a + b + c)`
= `(k(b + c - a) + k(c + a - b) + k(a + b - c))/(a + b + c)`
= `(k(b+ c- a + c + a - b + a + b - c))/(a +b + c)`
= `(k(a + b + c))/(a + b + c)`
= k.
Hence proved.
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