If {2+a}/a+{2+b}/b+{2+c}/c=4, then the value of \frac{ab+bc+ca}{abc} is

RRB Junior Engineer Stage 1 Model Papers 1

Question : 16 of 100

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{2+a}/a+{2+b}/b+{2+c}/c=4

, then the value of

{ab+bc+ca}/{abc}

Solution:

x + y + z = 1,1/x+1/y+1/z=1, xyz = –1

{xy+yz+zx}/{-1}=1

xy + yz + zx = – 1

(x + y + z)^2= 1

x^2+ y^2+ z^2+ 2xy + 2yz + 2zx = 1

x^2+ y^2+z^2+2(–1) = 1

x^2+ y^2+z^2= 3

x^3+ y^3+ z^3– 3xyz= (x + y + z) (x^2+ y^2+z^2+ xy – yz – zx)

x^3+ y^3+ z^3– 3 (–1) = (1) [ (3 – (–1)]

x^3+ y^3+ z^3+ 3 = 4

= 4 – 3 = 1

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