(343) 11/3=
Chapter 1 class 9th
Answers
Step-by-step explanation:
343×343+343×113+113×113
343×343×343−113×113×113
=\frac{343^{3}-113^{3}}{343^{2}+343\times 113+113^{2}}=
343
2
+343×113+113
2
343
3
−113
3
\begin{gathered}By \: algebraic \: identity :\\ a^{3}-b^{3}= (a-b)(a^{2}+ab+b^{2}\end{gathered}
Byalgebraicidentity:
a
3
−b
3
=(a−b)(a
2
+ab+b
2
\begin{gathered}Here , \\a = 343, \: b = 113\end{gathered}
Here,
a=343,b=113
= \frac{(343-113)(343^{2}+343\times 113+113^{2})}{(343^{2}+343\times 113+113^{2})}=
(343
2
+343×113+113
2
)
(343−113)(343
2
+343×113+113
2
)
\begin{gathered}= 343-113\\=220\end{gathered}
=343−113
=220
Therefore.,
Value \: of \:\frac{343\times 343\times 343 - 113\times 113\times 113}{343\times 343+343\times 113+113\times 113}= 220Valueof
343×343+343×113+113×113
343×343×343−113×113×113
=220