Question 120

If a + b + c = 1, ab + bc + ca = -1 and abc = -1, then the value of a$$^{3} + b^{3}+c^{3}$$ is:

Solution

Given : $$(a+b+c)=1$$ ----------(i) and $$(ab+bc+ca)=-1$$ and $$abc=-1$$ -------------(ii)

Squaring equation (i), we get :

=> $$(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)$$

=> $$(1)^2=(a^2+b^2+c^2)+2(-1)$$

=> $$a^2+b^2+c^2=1+2=3$$ -----------(iii)

Also, $$a^3+b^3+c^3=3abc+(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$$

= $$3(-1)+(1)\times[3-(-1)]$$

= $$-3+4=1$$

=> Ans - (A)

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