Question 34

If $$x^{3} - y^{3} = 112$$ and $$x - y = 4$$, then what is the value of $$x^{2} + y^{2}$$?

Solution

Given : $$x^3-y^3=112$$ --------------(i)

Also, $$x-y=4$$ -------------(ii)

Cubing both sides, we get :

=> $$(x-y)3=(4)^3$$

=> $$(x^3-y^3)-3(x)(y)(x-y)=64$$

Substituting values from equations (i) and (ii),

=> $$112-3xy(4)=64$$

=> $$12xy=112-64=48$$

=> $$xy=\frac{48}{12}=4$$ -----------(iii)

Now, squaring equation (ii), we get :

=> $$x^2+y^2-2xy=16$$

=> $$x^2+y^2=16+8=24$$

=> Ans - (C)

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