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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