Question 79

If $$a + b = 7, b + c = -3, c + a = -4$$, then $$a^3 + b^3 + c^3 =$$

Solution

Given,

$$a+b=7$$ ............(1)

$$b+c=-3$$ .........(2)

$$c+a=-4$$ .........(3)

Adding (1), (2) and (3), we get

$$2a+2b+2c=0$$

$$\Rightarrow$$ $$a+b+c=0$$ ........(4)

From (1) and (4), $$c=-7$$

From (2) and (4), $$a=3$$

From (3) and (4), $$b=4$$

$$\therefore\ $$ $$a^3+b^3+c^3=3^3+4^3+\left(-7\right)^3=27+64-343=-252$$

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