Question 133

If $$a + b + c = - 11$$, then what is the value of $$\ (a + 4)^{3}+(b+ 5)^{3}+(c + 2)^{3}-3(a + 4)(b + 5)(c + 2)\ $$?

Solution

Given : $$a+b+c=-11$$

=> $$a+b+c+11=0$$

=> $$(a+4)+(b+5)+(c+2)=0$$

Let $$(a+4)=x$$, $$(b+5)=y$$ and $$(c+2)=z$$

=> $$x+y+z=0$$ -----------(i)

To find : $$\ (a + 4)^{3}+(b+ 5)^{3}+(c + 2)^{3}-3(a + 4)(b + 5)(c + 2)\ $$

= $$x^3+y^3+z^3-3xyz$$

= $$(x+y+z)(x^2+y^2+z^2-xy-yz-zx)$$

Substituting value from equation (i), we get :

= $$(0)(x^2+y^2+z^2-xy-yz-zx)=0$$

=> Ans - (C)

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