SSC MTS Model Paper 5

Question : 42 of 148

Marks: +1, -0

If x = a(b − c), y = b(c − a) and z = c(a − b), then

( { x } /{ a } ) ^ { 3 } + ( { y }/ { b } ) ^ { 3 } + ( { z }/ { c } \) ^ { 3 } = ?

Solution:

{ x }/ { a } = ( b - c ) , { y }/ { b } = ( c - a ) , { z } /{ c } = ( a - b )

a + b + c = 0

then

a ^ { 3 } + b ^ { 3 } + c ^ { 3 } = 3 a b c

∴ { { x } }/ { { a } } + { { y } }/ { { b } } + { { z } }/ { { c } }

= b − c + c − a + a − b = 0
and

( { x } /{ a } ) ^ { 3 } + ( { y }/ { b } ) ^ { 3 } + ( { z } /{ c } ) ^ { 3 } = { 3 x y z }/ { a b c }

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