Question 176
If 5x + 9y = 5 and $$125x^{3}$$ + $$729y^{3}$$ = 120 then the value of the product of x and y is
Solution
Expression : $$5x + 9y = 5$$
Cubing both sides, we get :
=> $$(5x + 9y)^3 = 125$$
=> $$125x^3 + 729y^3 + 135xy(5x+9y) = 125$$
=> $$125x^3 + 729y^3 + 135xy*5 = 125$$
Since, $$125x^{3}$$ + $$729y^{3} = 120$$
=> $$xy = \frac{5}{5*135} = \frac{1}{135}$$
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