SSC CPO SI and ASI Model Paper 3

Question : 105 of 200

Marks: +1, -0

If a + b + c = 10,

a^2+ b^2+ c^2

= 38 and

a^3 + b^3 + c^3= 160

then abc = ?

Solution:

(4)

(a+b+c)^2 =100

⇒a^2+ b^2+ c^2+2 (ab + bc + ca)=100

⇒2 (ab + b + ca) = 100 – 38 =62

⇒ ab + bc + ca = 31
Also,

a^3+ b^3+ c^3–3abc = (a + b + c) (a^2+b^2+ c^2–ab–bc–ca)

160–3abc = 10(38 – 31)
⇒ 3abc = 90
⇒abc = 30

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