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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