Find the value of 27x3 + 8y?, if 3x + 2y = 7 and xy = 2
Answers
Answer:
\begin{gathered}\red{\underline{Given}} \colon \\\\ 3x-2y= 5\\xy=6\end{gathered}
Given
:
3x−2y=5
xy=6
\begin{gathered}\red{\underline{Solution\colon}}\\ We\: know \: \\\\a^{3}\: - \:b^{3} = (a-b)(a^{2}+ab+b^{2})\\\\ Now,\\\\ 27x^{3}-8y^{3} = (3x)^{3}-(2y)^{3} \\ where\: a = 3x \: and \:b= 2y\end{gathered}
Solution:
Weknow
a
3
−b
3
=(a−b)(a
2
+ab+b
2
)
Now,
27x
3
−8y
3
=(3x)
3
−(2y)
3
wherea=3xandb=2y
=> (3x-2y){(3x)²+(2y)²+(3x.2y)}
[*(a-b)² = a²+b²-2ab
*(a-b)²+2ab = a²+b²-2ab+2ab
*(a-b)²+2ab= a²+b²]
=> (3x-2y){(3x-2y)²+2×3x×2y+(6xy)}
=> (3x-2y){(3x-2y)²+12xy+6xy}
=> (3x-2y){(3x-2y)²+18xy}
put the values in equation :
=> (5){(5)²+18×6}
=> 5{25+108}
=> 5{133}
=> 665
\red{\bold{\underline{Answer}}}
Answer
\green{\boxed{value\: = \: 665}}
value=665