If 5x + 9y = 5 and 125x^3 + 729y^3 = 120,then | vedclass

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(B) Given equations are:
$5x + 9y = 5$ ---$(1)$
$125x^3 + 729y^3 = 120$ ---$(2)$
We know the algebraic identity: $(a + b)^3 = a^3 + b^3 + 3ab(a + b

Vedclass · Accepted Answer

$\frac{1}{135}$

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(B) Given equations are:
$5x + 9y = 5$ ---$(1)$
$125x^3 + 729y^3 = 120$ ---$(2)$
We know the algebraic identity: $(a + b)^3 = a^3 + b^3 + 3ab(a + b)$.
Let $a = 5x$ and $b = 9y$. Then $a^3 = 125x^3$ and $b^3 = 729y^3$.
Cubing equation $(1)$ on both sides:
$(5x + 9y)^3 = 5^3$
$(5x)^3 + (9y)^3 + 3(5x)(9y)(5x + 9y) = 125$
$125x^3 + 729y^3 + 135xy(5x + 9y) = 125$
Substitute the values from equation $(1)$ and $(2)$ into the expanded form:
$120 + 135xy(5) = 125$
$120 + 675xy = 125$
$675xy = 125 - 120$
$675xy = 5$
$xy = \frac{5}{675}$
$xy = \frac{1}{135}$

If $5x + 9y = 5$ and $125x^3 + 729y^3 = 120$,then the value of the product of $x$ and $y$ is:

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