Math, asked by prem772, 1 year ago

B. If x + 2y = 8 and xy = 6 find the value of x^3+8y^3​


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Answers

Answered by gujjarankit
3

we can assume the value of x & y

×y =6 the value ×&y maybe (1,6) (6,1)(3,2)(2,3)

by taking x=6 & y = 1 ,value fit in the equation

thus x^3+8y^3 = (6)^3 + 8(1)^3

=216 + 8

=224


prem772: my answer is write. i wanna check my answer
Answered by Pricilla
8

SOLUTION :-

 \underline{ \huge{ \bf{ \sf{ \:  \: Given \:  \: }}}  : \to}

 \rm{x + 2y = 8} \\  \\  \rm{xy = 6}

 \underline{ \huge{ \bf{ \sf{ \:  \: Now, \:  \: }}}  }

 \rm{ \:  \:  \:  \:  \:  x {}^{3}  + 8y {}^{3} } \\  \\  \rm{ = x {}^{3} + (2y) {}^{3}  } \\  \\ \rm{ = (x + 2y)(x {}^{2}  -  2xy  + 4y {}^{2}) } \\  \\ \rm{ = (x + 2y)[(x + 2y) {}^{2} - 6xy] }

 \underline{ \huge{ \bf{ \sf{ \:  \: </strong><strong>P</strong><strong>utting \:  \: the \:  \: values \:  \: }}}}

 \rm{(x + 2y)((x + 2y) {}^{2}  - 5xy)} \\  \\ \rm{ = (8) \times[ (8) {}^{2} - 6 \times 6] } \\  \\ \rm{ = 8 \times (64 - 36)} \\  \\ \rm{ = 8 \times 28} \\  \\ \rm{ =224}

\rm{ \therefore \:  \:  \: If \:  \:  \: x + 2y = 8 \:  \:  \: and \:  \:  \: xy = 6 \:  \:  \: then \:  \: \:  the} \\  \\  \:  \:  \:  \:  \:  \: \rm{value \:  \:  \: of \:  \:  \:   \underline{\bf{ \:  \: x {}^{3}  + 8y {}^{3}  = 224 \:  \: }}}

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