Question 86

If x + y = 5, $$x^{3} + y^{3}$$ = 35, then what is the positive difference between x and y?

Solution

Given : $$x^3+y^3=35$$ ----------(i)

and $$x+y=5$$ -------(ii)

Cubing both sides,

=> $$(x+y)^3=(5)^3$$

=> $$x^3+y^3+3xy(x+y)=125$$

Using equations (i) and (ii), we get :

=> $$35+3xy(5)=125$$

=> $$15xy=125-35=90$$

=> $$xy=\frac{90}{15}=6$$ -----------(iii)

Using, $$(x-y)^2=(x+y)^2-4xy$$

Using equations (ii) and (iii), we get :

=> $$(x-y)^2=(5)^2-4(6)$$

=> $$(x-y)^2=25-24=1$$

=> $$x-y=\sqrt1=1$$

=> Ans - (B)

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