Question

If x and y are two positive real numbers such that

8x^3 + 27y^3 = 730

2x^2y + 3xy^2 = 15

then show that 2x + 3y = 10


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Answer 1

Given,

$\displaystyle\longrightarrow\sf{8x^3+27y^3=730\quad\quad\dots(1)}$

And,

$\displaystyle\longrightarrow\sf{2x^2y+3xy^2=15\quad\quad\dots(2)}$

Add (1) to 18 times (2), i.e.,

$\displaystyle\longrightarrow\sf{(1)+18\times(2)}$

$\displaystyle\longrightarrow\sf{8x^3+27y^3+18(2x^2y+3xy^2)=730+18\times15}$

$\displaystyle\longrightarrow\sf{8x^3+36x^2y+54xy^2+27y^3=730+270}$

$\displaystyle\longrightarrow\sf{(2x)^3+3\cdot(2x)^2\cdot3y+3\cdot2x\cdot(3y)^2+(3y)^3=1000}$

$\displaystyle\longrightarrow\sf{(2x+3y)^3=10^3}$

$\displaystyle\longrightarrow\sf{\underline{\underline{2x+3y=10}}}$

Done!

Answer 2

Answer:

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Step-by-step explanation:

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