please tell me how to solve this problem please
Answers
Answer with Explanation :
taking LCM
{here i = √(-1) , therefore i²=(√-1)²=-1}
Hence is a real number.
Step-by-step explanation:
(
7
−i
3
7
+i
3
)+(
7
+i
3
7
−i
3
)
taking LCM
= (\frac{( \sqrt{7} + i \sqrt{3} )( \sqrt{7} + i \sqrt{3} ) + ( \sqrt{7} - i \sqrt{3})(7 - i \sqrt{3} ) }{(7 - i \sqrt{3})(7 +i \sqrt{3} )} )=(
(7−i
3
)(7+i
3
)
(
7
+i
3
)(
7
+i
3
)+(
7
−i
3
)(7−i
3
)
)
= ( \frac{ {( \sqrt{7} + i \sqrt{3}) }^{2} + ( \sqrt{7} - i \sqrt{3} ) ^{2} }{( { \sqrt{7} )}^{2} - {(i \sqrt{3}) }^{2} } )=(
(
7
)
2
−(i
3
)
2
(
7
+i
3
)
2
+(
7
−i
3
)
2
)
= ( \frac{ {( \sqrt{7} ) ^{2}+ 2 \times ( \sqrt{7})(i \sqrt{3} )} + ({ \sqrt{3} i} )^{2} + ( \sqrt{7} )^{2} - 2 \times ( \sqrt{7} ) (i \sqrt{3} ) + {(i \sqrt{3} )}^{2} } {7 + 3} )=(
7+3
(
7
)
2
+2×(
7
)(i
3
)+(
3
i)
2
+(
7
)
2
−2×(
7
)(i
3
)+(i
3
)
2
)
= (\frac{7 - 3 + 7 - 3}{10} )=(
10
7−3+7−3
)
= ( \frac{4 + 4}{10} ) = ( \frac{4}{5} )=(
10
4+4
)=(
5
4
)
{here i = √(-1) , therefore i²=(√-1)²=-1}
Hence (\frac{4}{5})(
5
4
) is a real number.