Question 4

What will be the value of $$a^{3}+b^{3}$$ ,if $$a^{2}+b^{2} =32$$ and $$a+b=8$$ ?

Solution

Given : $$a^2+b^2=32$$ ------------(i)

and $$a+b=8$$ ---------(ii)

Squaring both sides,

=> $$a^2+b^2+2ab=64$$

Substituting value from equation (i), => $$32+2ab=64$$

=> $$2ab=64-32=32$$

=> $$ab=\frac{32}{2}=16$$ ------------(iii)

$$\therefore$$ $$a^{3}+b^{3}$$

= $$(a+b)(a^2+b^2-ab)$$

Substituting values from equation (i), (ii) and (iii),

= $$(8)(32-16)$$

= $$8\times16=128$$

=> Ans - (C)

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