1.

If 2x+3y = 13 and XY = 6,find the value of 8x^3+27y^3..no spam.........​

Answer»

\huge{\mathbb{\red{ANSWER:-}}}

Given :-

\sf{(2x + 3y) = 13 \: , \: xy = 6}

To FIND :-

\sf{(8x^{3} + 27y^{3}) = ? \: }

USING Identity :-

\sf{(a + b)^{3} = a^{3} + b^{3} + 3ab(a + b)}

SOLUTION :-

\sf{(2x + 3y) = 13}

Doing Cube both SIDE -

\sf{(2x + 3y)^{3} = (13)^{3}}

\sf{(2x)^{3} + (3y)^{3} + 3(2x)(3y)(2x + 3y) = 2197}

\sf{8x^{3} + 27y^{3} + 3(6xy)(13) = 2197}

\sf{8x^{3} + 27y^{3} + 18(6)(13) = 2197}

\sf{8x^{3} + 27y^{3} + 108(13) = 2197}

\sf{8x^{3} + 27y^{3} = 13(169) - 13(108)}

\sf{8x^{3} + 27y^{3} = 13(169 - 108)}

\sf{8x^{3} + 27y^{3} = 13(61)}

\sf{8x^{3} + 27y^{3} = 793}

Result :-

\sf{Value \: of \: (8x^{3} + 27y^{3}) \: is \: 793.}


Discussion

No Comment Found

Related InterviewSolutions